title: Australian Labor Party

text: In practice, the platform provides only general policy guidelines to Labor's federal, state and territory parliamentary leaderships. The policy Labor takes into an election campaign is determined by the Cabinet (if the party is in office) or the Shadow Cabinet (if it is in opposition), in consultation with key interest groups within the party, and is contained in the parliamentary Leader's policy speech delivered during the election campaign. When Labor is in office, the policies it implements are determined by the Cabinet, subject to the platform. Generally, it is accepted that while the platform binds Labor governments, how and when it is implemented remains the prerogative of the parliamentary caucus. It is now rare for the platform to conflict with government policy, as the content of the platform is usually developed in close collaboration with the party's parliamentary leadership as well as the factions. However, where there is a direct contradiction with the platform, Labor governments have sought to change the platform as a prerequisite for a change in policy. For example, privatisation legislation under the Hawke government occurred only after holding a special national conference to debate changing the platform.,


title: Australian Labor Party

text: The Australian Labor Party National Executive is the party's chief administrative authority, subject only to Labor's national conference. The executive is responsible for organising the triennial national conference; carrying out the decisions of the conference; interpreting the national constitution, the national platform and decisions of the national conference; and directing federal members.


title: Australian Labor Party

text: The party holds a national conference every three years, which consists of delegates representing the state and territory branches (many coming from affiliated trade unions, although there is no formal requirement for unions to be represented at the national conference). The national conference decides the party's platform, elects the national executive and appoints office-bearers such as the national secretary, who also serves as national campaign director during elections. The current national secretary is Paul Erickson. The most recent national conference was the 48th conference held in December 2018.


title: Australian Labor Party

text: The head office of the ALP, the national secretariat, is managed by the national secretary. It plays a dual role of administration and a national campaign strategy. It acts as a permanent secretariat to the national executive by managing and assisting in all administrative affairs of the party. As the national secretary also serves as national campaign director during elections, it is also responsible for the national campaign strategy and organisation.


title: Australian Labor Party

text: The elected members of the Labor party in both houses of the national Parliament meet as the Federal Parliamentary Labor Party, also known as the Australian Labor Party Caucus (see also caucus). Besides discussing parliamentary business and tactics, the Caucus also is involved in the election of the federal parliamentary leaders.


title: Australian Labor Party

text: Until 2013, the parliamentary leaders were elected by the Caucus from among its members. The leader has historically been a member of the House of Representatives. Since October 2013, a ballot of both the Caucus and by the Labor Party's rank-and-file members determined the party leader and the deputy leader. When the Labor Party is in government, the party leader is the Prime Minister and the deputy leader is the Deputy Prime Minister. If a Labor prime minister resigns or dies in office, the deputy leader acts as prime minister and party leader until a successor is elected. The deputy prime minister also acts as prime minister when the prime minister is on leave or out of the country. Members of the Ministry are also chosen by Caucus, though the leader may allocate portfolios to the ministers.


title: Australian Labor Party

text: Anthony Albanese is the leader of the federal Labor party, serving since 30 May 2019. The deputy leader is Richard Marles, also serving since 30 May 2019.


title: Australian Labor Party

text: The Australian Labor Party is a federal party, consisting of eight branches from each state and territory. While the National Executive is responsible for national campaign strategy, each state and territory are an autonomous branch and are responsible for campaigning in their own jurisdictions for federal, state and local elections. State and territory branches consist of both individual members and affiliated trade unions, who between them decide the party's policies, elect its governing bodies and choose its candidates for public office.


title: Australian Labor Party

text: Members join a state branch and pay a membership fee, which is graduated according to income. The majority of trade unions in Australia are affiliated to the party at a state level. Union affiliation is direct and not through the Australian Council of Trade Unions. Affiliated unions pay an affiliation fee based on the size of their membership. Union affiliation fees make up a large part of the party's income. Other sources of funds for the party include political donations and public funding.


title: Australian Labor Party

text: Members are generally expected to attend at least one meeting of their local branch each year, although there are differences in the rules from state to state. In practice only a dedicated minority regularly attend meetings. Many members are only active during election campaigns.


title: Australian Labor Party

text: The members and unions elect delegates to state and territory conferences (usually held annually, although more frequent conferences are often held). These conferences decide policy, and elect state or territory executives, a state or territory president (an honorary position usually held for a one-year term), and a state or territory secretary (a full-time professional position). However, ACT Labor directly elects its president. The larger branches also have full-time assistant secretaries and organisers. In the past the ratio of conference delegates coming from the branches and affiliated unions has varied from state to state, however under recent national reforms at least 50% of delegates at all state and territory conferences must be elected by branches.


title: Australian Labor Party

text: In some states it also contests local government elections or endorses local candidates. In others it does not, preferring to allow its members to run as non-endorsed candidates. The process of choosing candidates is called preselection. Candidates are preselected by different methods in the various states and territories. In some they are chosen by ballots of all party members, in others by panels or committees elected by the state conference, in still others by a combination of these two.


title: Australian Labor Party

text: The Country Labor party was an Australian political party affiliated and/or a division of the Australian Labor Party (ALP). Although not expressly defined, Country Labor operates mainly within rural New South Wales, and is mainly seen as an extension of the New South Wales branch that operates in rural electorates.


title: Australian Labor Party

text: Country Labor is a subsection of the ALP, and is used as a designation by candidates contesting elections in rural areas. The Country Labor Party is registered as a separate party in New South Wales, and is also registered with the Australian Electoral Commission (AEC) for federal elections. It does not have the same status in other states and, consequently, that designation cannot be used on the ballot paper.


title: Australian Labor Party

text: The creation of a separation designation for rural candidates was first suggested at the June 1999 ALP state conference in New South Wales. In May 2000, following Labor's success at the 2000 Benalla by-election in Victoria, Kim Beazley announced that the ALP intended to register a separate "Country Labor Party" with the AEC; this occurred in October 2000. The Country Labor designation is most frequently used in New South Wales. According to the ALP's financial statements for the 2015–16 financial year, NSW Country Labor had around 2,600 members (around 17 percent of the party total), but almost no assets. It recorded a severe funding shortfall at the 2015 New South Wales election, and had to rely on a $1.68-million loan from the party proper to remain solvent. It had been initially assumed that the party proper could provide the money from its own resources, but the NSW Electoral Commission ruled that this was impermissible because the parties were registered separately. Instead the party proper had to loan Country Labor the required funds at a commercial interest rate.


title: Australian Labor Party

text: Australian Young Labor is the youth wing of the Australian Labor Party, where all members under age 26 are automatically members. It is the peak youth body within the ALP. Former presidents of AYL have included former NSW Premier Bob Carr, Federal Manager of Opposition Business Tony Burke, former Special Minister of State Senator John Faulkner, former Australian Workers Union National Secretary, current Member for Maribyrnong and former Federal Labor Leader Bill Shorten as well as dozens of State Ministers and MPs. The current National President is Jason Byrne from South Australia.


title: Australian Labor Party

text: The Australian Labor Party is beginning to formally recognise single interest groups within the party. The national platform currently encourages state branches to formally establish these groups known as policy action caucuses. Examples of such groups include the Labor Environment Action Network, Rainbow Labor, Labor For Choice, Labor Women's Network, Labor for Drug Law Reform Labor for Refugees, Labor for Housing, Labor Teachers Network, Aboriginal Labor Network, and recently, Labor Enabled - the action group for Disability Advocacy The Tasmanian Branch of the Australian Labor Party recently gave these groups voting and speaking rights at their state conference.


title: Australian Labor Party

text: Labor's constitution has long stated: "The Australian Labor Party is a democratic socialist party and has the objective of the democratic socialisation of industry, production, distribution and exchange, to the extent necessary to eliminate exploitation and other anti-social features in these fields". This "socialist objective" was introduced in 1921, but was later qualified by two further objectives: "maintenance of and support for a competitive non-monopolistic private sector" and "the right to own private property". Labor governments have not attempted the "democratic socialisation" of any industry since the 1940s, when the Chifley Government failed to nationalise the private banks, and in fact have privatised several industries such as aviation and banking. Labor's current National Platform describes the party as "a modern social democratic party". Observers have also described it as social-democratic in contrast to democratic socialism.


title: Australian Labor Party

text: The Labor Party has always had a left wing and a right wing, but since the 1970s it has been organised into formal factions, to which party members may belong and often pay an additional membership fee. The two largest factions are the Labor Left and the Labor Right, led by Anthony Albanese and Bill Shorten, respectively. The Labor Right generally supports free-market policies and the US alliance and tends to be conservative on some social issues, whilst the Labor Left favours more state intervention in the economy, is generally less enthusiastic about the US alliance and is often more progressive on social issues. The national factions are themselves divided into sub-factions, primarily state-based such as Centre Unity in New South Wales and Labor Forum in Queensland. Those factions tend to occupy social-liberal, and social democratic positions.


title: Australian Labor Party

text: Some trade unions are affiliated with the Labor Party and are also factionally aligned. The largest unions supporting the right faction are the Australian Workers' Union (AWU), the Shop, Distributive and Allied Employees' Association (SDA) and the Transport Workers Union (TWU). Important unions supporting the left include the Australian Manufacturing Workers Union (AMWU), United Workers Union, the Construction, Forestry, Maritime, Mining and Energy Union (CFMMEU) and the Community and Public Sector Union (CPSU).


title: Australian Labor Party

text: Preselections are usually conducted along factional lines, although sometimes a non-factional candidate will be given preferential treatment (this happened with Cheryl Kernot in 1998 and again with Peter Garrett in 2004). Deals between the factions to divide up the safe seats between them often take place. Preselections, particularly for safe Labor seats, can sometimes be strongly contested. A particularly fierce preselection sometimes gives rise to accusations of branch stacking (signing up large numbers of nominal party members to vote in preselection ballots), personation, multiple voting and, on occasions, fraudulent electoral enrolment. Trade unions were in the past accused of giving inflated membership figures to increase their influence over preselections, but party rules changes have stamped out this practice. Preselection results are sometimes challenged, and the National Executive is sometimes called on to arbitrate these disputes.


title: Australian Labor Party

text: For the 2015–2016 financial year, the top ten disclosed donors to the ALP were the Health Services Union NSW ($389,000), Village Roadshow ($257,000), Electrical Trades Union of Australia ($171,000), National Automotive Leasing and Salary Packaging Association ($153,000), Westfield Corporation ($150,000), Randazzo C&G Developments ($120,000), Macquarie Telecom ($113,000), Woodside Energy ($110,000), ANZ Bank ($100,000) and Ying Zhou ($100,000), all significantly lower than the 2014 donations by a Chinese donor Zi Chun Wang, which at $850,000 was the largest donation to any political party in the 2013-2014 financial year. At least one newspaper report queried the identity of this donor stating "news archive searches do not produce results for this name, suggesting Wang operates under another name". Another report mentions that in addition to a hotel and a travel agency, the donor's listed address at the Old Communist Cadres Activity Centre in Shijiazhuang houses several Chinese government entities, stating also that another publisher "tried many times without success" to contact the donor on the phone number listed in the donation return form.


title: Australian Labor Party

text: The Labor Party also receives undisclosed funding through several methods, such as "associated entities". John Curtin House, Industry 2020, IR21 and the Happy Wanderers Club are entities which have been used to funnel donations to the Labor Party without disclosing the source.


title: Australian Labor Party

text: A 2019 report found that the Labor Party received $33,000 from pro-gun groups during the 2011–2018 periods, however, the Coalition received over $82,000 in donations from pro-gun groups, more than doubling Labor's pro-gun donors.


title: Australian Labor Party

text: Ormonde, Paul (1982). "A Foolish Passionate Man: a biography of Jim Cairns". Ringwood, Vic, Australia: Penguin Books. ISBN 014005975X.


title: Australian Labor Party

text: Charlesworth, M. J. (2000) Ormonde, Paul (Ed). "Santamaria : the politics of fear : critical reflections". Richmond, Vic.: Spectrum Publications. ISBN 0867862947


title: Glenne Headly

text: Glenne Aimee Headly (March 13, 1955 – June 8, 2017) was an American actress. She was widely known for her roles in "Dirty Rotten Scoundrels", "Dick Tracy", and "Mr. Holland's Opus". Headly received a Theatre World Award and four Joseph Jefferson Awards and was nominated for two Primetime Emmy Awards.


title: Glenne Headly

text: In 2017, she starred in "The Circle" and "Just Getting Started", the latter marking her final film role, released six months after her death. She also starred with Ed Begley Jr. and Josh Hutcherson in "Future Man", Hulu's half-hour comedy television series produced by Seth Rogen and Evan Goldberg; she died on June 8, 2017, mid-way through filming the series.


title: Glenne Headly

text: Headly was born on March 13, 1955, in New London, Connecticut. Her first years were spent living in the care of her mother, Joan Ida Headly (née Sniscak), in San Francisco, and her maternal grandmother in Lansford, Pennsylvania.


title: Glenne Headly

text: Early in her elementary school years, she joined her mother, who was then living in Greenwich Village. She studied ballet at the Robert Joffrey school of ballet and modern dance at the Martha Graham Studios. In New York, she attended public schools, including P. S. 41, where she was placed in a class for intellectually gifted children. There, a fifth-grade teacher introduced her to the work of Jacques Cousteau in an oceanography class, triggering a lifelong interest in preserving the natural world. She later went on to the High School of Performing Arts, majoring in drama and graduating with honors.


title: Glenne Headly

text: Rather than continuing to study the dramatic arts, she attended the American College of Switzerland, a small college in Leysin from which she graduated with a bachelor's degree. Soon after, she moved to New York, taking day jobs as a waitress so she could work nights in the theater for little or no salary. Later, she moved to Chicago, where she joined the New Works Ensemble at the St. Nicholas Theatre. She was eventually cast in a Goodman Theatre production of "Curse of the Starving Class", directed by Robert Falls and co-starring John Malkovich.


title: Glenne Headly

text: While appearing on the Chicago stage in "Curse of the Starving Class", Headly was asked to join the Steppenwolf Theatre ensemble, which was looking to expand. She also appeared in several other productions. In Chicago, she was nominated for five Joseph Jefferson awards, and won three for best supporting actress. She received her Actors' Equity card when cast by Vivian Matalon in a summer theatre production of "Charley's Aunt", and joined SAG when Arthur Penn wrote a breakout role for her in the film "Four Friends".


title: Glenne Headly

text: On August 2, 1982, Headly married fellow ensemble member John Malkovich. Soon after, she replaced Ellen Barkin in "Extremities" off-Broadway. She then was cast in "The Philanthropist", also off-Broadway, and won a Theatre World Award for best newcomer. In New York, she appeared in "Balm in Gilead" with her fellow Steppenwolf Theatre members, and in "Arms and the Man", on Broadway, with Kevin Kline and Raul Julia.


title: Glenne Headly

text: Headly played several supporting roles in such films as "Making Mr. Right", "Paperhouse", "Seize the Day" and "Nadine", but her role in "Dirty Rotten Scoundrels" (1988), with Steve Martin and Michael Caine, truly launched her film career. In 1988, Headly was named Most Promising New Actress by the Chicago Film Critics Association. That same year, Headly divorced Malkovich after he had an affair with Michelle Pfeiffer during the filming of "Dangerous Liaisons".


title: Glenne Headly

text: In 1989, Headly played the role of Elmira Boot Johnson in the critically acclaimed TV miniseries "Lonesome Dove", a part for which she received her first of two Emmy Awards nominations for best supporting actress in a television movie.


title: Glenne Headly

text: Headly then was cast by Warren Beatty to appear as Tess Trueheart in "Dick Tracy". She next starred with Demi Moore and Bruce Willis in "Mortal Thoughts", directed by Alan Rudolph. In 1992, she worked on a small Canadian film called "Ordinary Magic", and on the first day of filming, met her future husband Byron McCulloch, whom she married in 1993. She also co-starred with Ted Danson and Macaulay Culkin in the 1994 comedy "Getting Even with Dad".


title: Glenne Headly

text: Headly appeared in "Mr. Holland's Opus", "Sgt. Bilko", "What's the Worst That Could Happen?", "Breakfast of Champions", "Around the Bend", "2 Days in the Valley", and others.


title: Glenne Headly

text: Headly appeared in the television movies "Winchell", "And the Band Played On", "Pronto", "My Own Country", and "Women vs. Men". Headly received her second of two Emmy Awards nominations for best supporting actress in a television movie for "Bastard Out of Carolina" (1996). She appeared as Julie Andrews and Christopher Plummer's daughter in the 2001 live telecast of the play "On Golden Pond" for CBS. She was cast in the series "Encore! Encore!", starring Nathan Lane and Joan Plowright, from 1998 to 1999, and had recurring roles as Dr. Abby Keaton on "ER" from 1996 to 1997 and as Leland Stottlemeyer's wife, Karen, on "Monk".


title: Glenne Headly

text: In 2004, she played the mother of Lindsay Lohan's character in "Confessions of a Teenage Drama Queen". She appeared in the films "The Amateurs" (2005), "The Namesake" (2006), "Comeback Season" (2006), "" (2008), "The Joneses" (2009), and "Don Jon" (2013).


title: Glenne Headly

text: Headly appeared in the film "Strange Weather" (2016) and in the HBO limited series "The Night Of" (2016).


title: Glenne Headly

text: Headly and Ed Begley Jr. were cast in lead roles with Josh Hutcherson in "Future Man", Hulu's half-hour comedy television series produced by Seth Rogen and Evan Goldberg. Headly died on June 8, 2017, during filming of the series. At the time of her death, she had filmed five episodes of the planned 13-episode season order. Producers stated that she would not be recast and that the episodes she filmed will air, leaving the writers to rework the episodes in which she was due to appear.


title: Glenne Headly

text: Headly was an ensemble member of the Steppenwolf Theatre Company from 1979 until 2005, although she never returned to Chicago to do a play after the late 1980s, believing that such a move would uproot and be disruptive to her family. She took a break from the stage altogether for 10 years until 1999, when she starred with Miranda Richardson in Wallace Shawn's "Aunt Dan and Lemon", which premiered at the Almeida Theatre in London.


title: Glenne Headly

text: In 1983, Headly appeared in Christopher Hampton's "The Philanthropist" at the Manhattan Theater Club in New York.


title: Glenne Headly

text: In 1984, Headly appeared in Lanford Wilson's "Balm in Gilead" presented by the Circle Repertory Company and the Steppenwolf Theater Ensemble.


title: Glenne Headly

text: In 1985, Headly starred as Raina in George Bernard Shaw's "Arms and the Man", directed by John Malkovich, in New York.


title: Glenne Headly

text: In 2000, Headly starred as Ellen in "Detachments" at the Tiffany Theater in Los Angeles, written and directed by Colleen Dodson-Baker.


title: Glenne Headly

text: In 2001, Headly starred as Angela Kennedy Lipsky in the premiere of "My Brilliant Divorce" at the Druid Theatre in Galway, Ireland.


title: Glenne Headly

text: In 2003, Headly starred with David Hyde Pierce in "The Guys" as part of a revolving cast at the Actors' Gang in Los Angeles. She also appeared in Malkovich's production of Shaw's "Arms and the Man", with Kevin Kline at New York City's Circle in the Square Uptown.


title: Glenne Headly

text: In 2012, Headly played Eva White in the Geffen Playhouse's production of "The Jacksonian", written by Beth Henley.


title: Glenne Headly

text: Headly died of complications from a pulmonary embolism on June 8, 2017, at the age of 62, in Santa Monica, California.


title: Riemann hypothesis

text: In mathematics, the Riemann hypothesis is the conjecture that the Riemann zeta function has its zeros only at the negative even integers and complex numbers with real part . Many consider it to be the most important unsolved problem in pure mathematics. It is of great interest in number theory because it implies results about the distribution of prime numbers. It was proposed by , after whom it is named.


title: Riemann hypothesis

text: The Riemann hypothesis and some of its generalizations, along with Goldbach's conjecture and the twin prime conjecture, make up Hilbert's eighth problem in David Hilbert's list of twenty-three unsolved problems; it is also one of the Clay Mathematics Institute's Millennium Prize Problems, which offers a million dollars to anyone who solves any of them. The name is also used for some closely related analogues, such as the Riemann hypothesis for curves over finite fields.


title: Riemann hypothesis

text: The Riemann zeta function ζ("s") is a function whose argument "s" may be any complex number other than 1, and whose values are also complex. It has zeros at the negative even integers; that is, ζ("s") = 0 when "s" is one of −2, −4, −6, ... These are called its "trivial zeros". The zeta function is also zero for other values of "s", which are called "nontrivial zeros". The Riemann hypothesis is concerned with the locations of these nontrivial zeros, and states that:


title: Riemann hypothesis

text: Thus, if the hypothesis is correct, all the nontrivial zeros lie on the "critical line" consisting of the complex numbers where "t" is a real number and "i" is the imaginary unit.


title: Riemann hypothesis

text: The Riemann zeta function is defined for complex "s" with real part greater than 1 by the absolutely convergent infinite series


title: Riemann hypothesis

text: Leonhard Euler already considered this series in the 1730s for real values of s, in conjunction with his solution to the Basel problem. He also proved that it equals the Euler product


title: Riemann hypothesis

text: The Riemann hypothesis discusses zeros outside the region of convergence of this series and Euler product. To make sense of the hypothesis, it is necessary to analytically continue the function to obtain a form that is valid for all complex "s". Because the zeta function is meromorphic, all choices of how to perform this analytic continuation will lead to the same result, by the identity theorem. A first step in this continuation observes that the series for the zeta function and the Dirichlet eta function satisfy the relation


title: Riemann hypothesis

text: within the region of convergence for both series. However, the zeta function series on the right converges not just when the real part of "s" is greater than one, but more generally whenever "s" has positive real part. Thus, the zeta function can be redefined as formula_4, extending it from to a larger domain: , except for the points where formula_5 is zero. These are the points formula_6 where formula_7 can be any nonzero integer; the zeta function can be extended to these values too by taking limits (see ), giving a finite value for all values of "s" with positive real part except for the simple pole at "s" = 1.


title: Riemann hypothesis

text: One may then define ζ("s") for all remaining nonzero complex numbers "s" ( and "s" ≠ 0) by applying this equation outside the strip, and letting ζ("s") equal the right-hand side of the equation whenever "s" has non-positive real part (and "s" ≠ 0).


title: Riemann hypothesis

text: If "s" is a negative even integer then ζ("s") = 0 because the factor sin(π"s"/2) vanishes; these are the "trivial zeros" of the zeta function. (If "s" is a positive even integer this argument does not apply because the zeros of the sine function are cancelled by the poles of the gamma function as it takes negative integer arguments.)


title: Riemann hypothesis

text: The value ζ(0) = −1/2 is not determined by the functional equation, but is the limiting value of ζ("s") as "s" approaches zero. The functional equation also implies that the zeta function has no zeros with negative real part other than the trivial zeros, so all non-trivial zeros lie in the "critical strip" where "s" has real part between 0 and 1.


title: Riemann hypothesis

text: Riemann's original motivation for studying the zeta function and its zeros was their occurrence in his explicit formula for the number of primes ("x") less than or equal to a given number "x", which he published in his 1859 paper "On the Number of Primes Less Than a Given Magnitude". His formula was given in terms of the related function


title: Riemann hypothesis

text: which counts the primes and prime powers up to "x", counting a prime power "p" as . The number of primes can be recovered from this function by using the Möbius inversion formula,


title: Riemann hypothesis

text: where the sum is over the nontrivial zeros of the zeta function and where Π is a slightly modified version of Π that replaces its value at its points of discontinuity by the average of its upper and lower limits:


title: Riemann hypothesis

text: The summation in Riemann's formula is not absolutely convergent, but may be evaluated by taking the zeros ρ in order of the absolute value of their imaginary part. The function li occurring in the first term is the (unoffset) logarithmic integral function given by the Cauchy principal value of the divergent integral


title: Riemann hypothesis

text: The terms li("x") involving the zeros of the zeta function need some care in their definition as li has branch points at 0 and 1, and are defined (for "x" > 1) by analytic continuation in the complex variable "ρ" in the region Re("ρ") > 0, i.e. they should be considered as . The other terms also correspond to zeros: the dominant term li("x") comes from the pole at "s" = 1, considered as a zero of multiplicity −1, and the remaining small terms come from the trivial zeros. For some graphs of the sums of the first few terms of this series see or .


title: Riemann hypothesis

text: This formula says that the zeros of the Riemann zeta function control the oscillations of primes around their "expected" positions. Riemann knew that the non-trivial zeros of the zeta function were symmetrically distributed about the line and he knew that all of its non-trivial zeros must lie in the range He checked that a few of the zeros lay on the critical line with real part 1/2 and suggested that they all do; this is the Riemann hypothesis.


title: Riemann hypothesis

text: The practical uses of the Riemann hypothesis include many propositions known to be true under the Riemann hypothesis, and some that can be shown to be equivalent to the Riemann hypothesis.


title: Riemann hypothesis

text: Riemann's explicit formula for the number of primes less than a given number in terms of a sum over the zeros of the Riemann zeta function says that the magnitude of the oscillations of primes around their expected position is controlled by the real parts of the zeros of the zeta function. In particular the error term in the prime number theorem is closely related to the position of the zeros. For example, if β is the upper bound of the real parts of the zeros, then


title: Riemann hypothesis

text: Von Koch (1901) proved that the Riemann hypothesis implies the "best possible" bound for the error of the prime number theorem. A precise version of Koch's result, due to , says that the Riemann hypothesis implies


title: Riemann hypothesis

text: where formula_16 is the prime-counting function, formula_17 is the logarithmic integral function, and formula_18 is the natural logarithm of "x".


title: Riemann hypothesis

text: The Riemann hypothesis implies strong bounds on the growth of many other arithmetic functions, in addition to the primes counting function above.


title: Riemann hypothesis

text: is valid for every "s" with real part greater than 1/2, with the sum on the right hand side converging, is equivalent to the Riemann hypothesis. From this we can also conclude that if the Mertens function is defined by


title: Riemann hypothesis

text: for every positive ε is equivalent to the Riemann hypothesis (J.E. Littlewood, 1912; see for instance: paragraph 14.25 in ). (For the meaning of these symbols, see Big O notation.) The determinant of the order "n" Redheffer matrix is equal to "M"("n"), so the Riemann hypothesis can also be stated as a condition on the growth of these determinants. The Riemann hypothesis puts a rather tight bound on the growth of "M", since disproved the slightly stronger Mertens conjecture


title: Riemann hypothesis

text: The Riemann hypothesis is equivalent to many other conjectures about the rate of growth of other arithmetic functions aside from μ("n"). A typical example is Robin's theorem, which states that if σ("n") is the sigma function, given by


title: Riemann hypothesis

text: for all "n" > 5040 if and only if the Riemann hypothesis is true, where γ is the Euler–Mascheroni constant.


title: Riemann hypothesis

text: A related bound was given by Jeffrey Lagarias in 2002, who proved that the Riemann hypothesis is equivalent to the statement that:


title: Riemann hypothesis

text: is true for all "n" ≥ "p"# where φ("n") is Euler's totient function and "p"# is the product of the first 120569 primes.


title: Riemann hypothesis

text: Another example was found by Jérôme Franel, and extended by Landau (see ). The Riemann hypothesis is equivalent to several statements showing that the terms of the Farey sequence are fairly regular. One such equivalence is as follows: if "F" is the Farey sequence of order "n", beginning with 1/"n" and up to 1/1, then the claim that for all ε > 0


title: Riemann hypothesis

text: For an example from group theory, if "g"("n") is Landau's function given by the maximal order of elements of the symmetric group "S" of degree "n", then showed that the Riemann hypothesis is equivalent to the bound


title: Riemann hypothesis

text: The Riemann hypothesis has various weaker consequences as well; one is the Lindelöf hypothesis on the rate of growth of the zeta function on the critical line, which says that, for any "ε" > 0,


title: Riemann hypothesis

text: The Riemann hypothesis also implies quite sharp bounds for the growth rate of the zeta function in other regions of the critical strip. For example, it implies that


title: Riemann hypothesis

text: The prime number theorem implies that on average, the gap between the prime "p" and its successor is log "p". However, some gaps between primes may be much larger than the average. Cramér proved that, assuming the Riemann hypothesis, every gap is "O"( log "p"). This is a case in which even the best bound that can be proved using the Riemann hypothesis is far weaker than what seems true: Cramér's conjecture implies that every gap is "O"((log "p")), which, while larger than the average gap, is far smaller than the bound implied by the Riemann hypothesis. Numerical evidence supports Cramér's conjecture.


title: Riemann hypothesis

text: Many statements equivalent to the Riemann hypothesis have been found, though so far none of them have led to much progress in proving (or disproving) it. Some typical examples are as follows. (Others involve the divisor function σ("n").)


title: Riemann hypothesis

text: is dense in the Hilbert space "L"(0,1) of square-integrable functions on the unit interval. extended this by showing that the zeta function has no zeros with real part greater than 1/"p" if and only if this function space is dense in "L"(0,1). This Nyman-Beurling criterion was strengthened by Baez-Duarte to the case where formula_43.


title: Riemann hypothesis

text: Weil's criterion is the statement that the positivity of a certain function is equivalent to the Riemann hypothesis. Related is Li's criterion, a statement that the positivity of a certain sequence of numbers is equivalent to the Riemann hypothesis.


title: Riemann hypothesis

text: That formula_48 has only simple zeros on the critical line is equivalent to its derivative having no zeros on the critical line.


title: Riemann hypothesis

text: The De Bruijn–Newman constant denoted by Λ and named after Nicolaas Govert de Bruijn and Charles M. Newman, is defined


title: Riemann hypothesis

text: that is parametrised by a real parameter "λ", has a complex variable "z" and is defined using a super-exponentially decaying function


title: Riemann hypothesis

text: Since the Riemann hypothesis is equivalent to the claim that all the zeroes of "H"(0, "z") are real, the Riemann hypothesis is equivalent to the conjecture that formula_53. Brad Rodgers and Terence Tao discovered the equivalence is actually formula_54 by proving zero to be the lower bound of the constant. Proving zero is also the upper bound would therefore prove the Riemann hypothesis. As of April 2020 the upper bound is formula_55.


title: Riemann hypothesis

text: Several applications use the generalized Riemann hypothesis for Dirichlet L-series or zeta functions of number fields rather than just the Riemann hypothesis. Many basic properties of the Riemann zeta function can easily be generalized to all Dirichlet L-series, so it is plausible that a method that proves the Riemann hypothesis for the Riemann zeta function would also work for the generalized Riemann hypothesis for Dirichlet L-functions. Several results first proved using the generalized Riemann hypothesis were later given unconditional proofs without using it, though these were usually much harder. Many of the consequences on the following list are taken from .


title: Riemann hypothesis

text: Some consequences of the RH are also consequences of its negation, and are thus theorems. In their discussion of the Hecke, Deuring, Mordell, Heilbronn theorem, say


title: Riemann hypothesis

text: The method of proof here is truly amazing. If the generalized Riemann hypothesis is true, then the theorem is true. If the generalized Riemann hypothesis is false, then the theorem is true. Thus, the theorem is true!!     (punctuation in original)


title: Riemann hypothesis

text: Care should be taken to understand what is meant by saying the generalized Riemann hypothesis is false: one should specify exactly which class of Dirichlet series has a counterexample.


title: Riemann hypothesis

text: investigated the problem of Hardy–Littlewood "2" and proved that for any ε > 0 there exists such formula_57 and "c" = "c"(ε) > 0, such that for formula_58 and formula_59 the inequality formula_60 is true. Selberg conjectured that this could be tightened to formula_61. proved that for a fixed ε satisfying the condition 0 < ε < 0.001, a sufficiently large "T" and formula_62, formula_63, the interval ("T", "T"+"H") contains at least "cH" log("T") real zeros of the Riemann zeta function formula_64 and therefore confirmed the Selberg conjecture. The estimates of Selberg and Karatsuba can not be improved in respect of the order of growth as "T" → ∞.


title: Riemann hypothesis

text: has the same zeros as the zeta function in the critical strip, and is real on the critical line because of the functional equation, so one can prove the existence of zeros exactly on the real line between two points by checking numerically that the function has opposite signs at these points. Usually one writes


title: Riemann hypothesis

text: where Hardy's Z function and the Riemann–Siegel theta function θ are uniquely defined by this and the condition that they are smooth real functions with θ(0)=0.


title: Riemann hypothesis

text: By finding many intervals where the function "Z" changes sign one can show that there are many zeros on the critical line. To verify the Riemann hypothesis up to a given imaginary part "T" of the zeros, one also has to check that there are no further zeros off the line in this region. This can be done by calculating the total number of zeros in the region using Turing's method and checking that it is the same as the number of zeros found on the line. This allows one to verify the Riemann hypothesis computationally up to any desired value of "T" (provided all the zeros of the zeta function in this region are simple and on the critical line).


title: Riemann hypothesis

text: Some calculations of zeros of the zeta function are listed below, where the "height" of a zero is the magnitude of its imaginary part, and the height of the "n"th zero is denoted by γ. So far all zeros that have been checked are on the critical line and are simple. (A multiple zero would cause problems for the zero finding algorithms, which depend on finding sign changes between zeros.) For tables of the zeros, see or .


title: Riemann hypothesis

text: A Gram point is a point on the critical line 1/2 + "it" where the zeta function is real and non-zero. Using the expression for the zeta function on the critical line, ζ(1/2 + "it") = "Z"("t")e, where Hardy's function, "Z", is real for real "t", and θ is the Riemann–Siegel theta function, we see that zeta is real when sin(θ("t")) = 0. This implies that θ("t") is an integer multiple of π, which allows for the location of Gram points to be calculated fairly easily by inverting the formula for θ. They are usually numbered as "g" for "n" = 0, 1, ..., where "g" is the unique solution of θ("t") = "n"π.


title: Riemann hypothesis

text: Gram observed that there was often exactly one zero of the zeta function between any two Gram points; Hutchinson called this observation Gram's law. There are several other closely related statements that are also sometimes called Gram's law: for example, (−1)"Z"("g") is usually positive, or "Z"("t") usually has opposite sign at consecutive Gram points. The imaginary parts γ of the first few zeros (in blue) and the first few Gram points "g" are given in the following table


title: Riemann hypothesis

text: A Gram point "t" is called good if the zeta function is positive at 1/2 + "it". The indices of the "bad" Gram points where "Z" has the "wrong" sign are 126, 134, 195, 211, ... . A "Gram block" is an interval bounded by two good Gram points such that all the Gram points between them are bad. A refinement of Gram's law called Rosser's rule due to says that Gram blocks often have the expected number of zeros in them (the same as the number of Gram intervals), even though some of the individual Gram intervals in the block may not have exactly one zero in them. For example, the interval bounded by "g" and "g" is a Gram block containing a unique bad Gram point "g", and contains the expected number 2 of zeros although neither of its two Gram intervals contains a unique zero. Rosser et al. checked that there were no exceptions to Rosser's rule in the first 3 million zeros, although there are infinitely many exceptions to Rosser's rule over the entire zeta function.


title: Riemann hypothesis

text: Gram's rule and Rosser's rule both say that in some sense zeros do not stray too far from their expected positions. The distance of a zero from its expected position is controlled by the function "S" defined above, which grows extremely slowly: its average value is of the order of (log log "T"), which only reaches 2 for T around 10. This means that both rules hold most of the time for small "T" but eventually break down often. Indeed, showed that both Gram's law and Rosser's rule fail in a positive proportion of cases. To be specific, it is expected that in about 73% one zero is enclosed by two successive Gram points, but in 14% no zero and in 13% two zeros are in such a Gram-interval on the long run.


title: Riemann hypothesis

text: Mathematical papers about the Riemann hypothesis tend to be cautiously noncommittal about its truth. Of authors who express an opinion, most of them, such as and , imply that they expect (or at least hope) that it is true. The few authors who express serious doubt about it include , who lists some reasons for skepticism, and , who flatly states that he believes it false, that there is no evidence for it and no imaginable reason it would be true. The consensus of the survey articles (, , and ) is that the evidence for it is strong but not overwhelming, so that while it is probably true there is reasonable doubt.


title: Riemann hypothesis

text: Some of the arguments for and against the Riemann hypothesis are listed by , , and , and include the following:


title: Riemann hypothesis

text: There are several nontechnical books on the Riemann hypothesis, such as , , , , and . The books , , , and give mathematical introductions, while , and are advanced monographs.


title: Agatha Christie's Poirot

text: Poirot (also known as Agatha Christie's Poirot) is a British mystery drama television programme that aired on ITV from 8 January 1989 to 13 November 2013. David Suchet starred as the eponymous detective, Agatha Christie's fictional Hercule Poirot. Initially produced by LWT, the series was later produced by ITV Studios. The series also aired on VisionTV in Canada and on PBS and A&E in the United States.


title: Agatha Christie's Poirot

text: The programme ran for 13 series and 70 episodes in total; each episode was adapted from a novel or short story by Christie that featured Poirot, and consequently in each episode Poirot is both the main detective in charge of the investigation of a crime (usually murder) and the protagonist who is at the centre of most of the episode's action. At the programme's conclusion, which finished with "" (based on the 1975 novel "Curtain", the final Poirot novel), every major literary work by Christie that featured the title character had been adapted.


title: Agatha Christie's Poirot

text: Clive Exton in partnership with producer Brian Eastman adapted the pilot. Together, they wrote and produced the first eight series. Exton and Eastman left "Poirot" after 2001, when they began work on "Rosemary & Thyme". Michele Buck and Damien Timmer, who both went on to form Mammoth Screen, were behind the revamping of the series. The episodes aired from series 9 in 2003 featured a radical shift in tone from the previous series. The humour of the earlier series was downplayed with each episode being presented as serious drama and saw the introduction of gritty elements not present in the Christie stories being adapted. Recurrent motifs in the additions included drug use, sex, abortion, homosexuality, and a tendency toward more visceral imagery. Story changes were often made to present female characters in a more sympathetic or heroic light, at odds with Christie's characteristic gender neutrality. The visual style of later episodes was correspondingly different: particularly, an overall darker tone; and austere modernist or Art Deco locations and decor, widely used earlier in the series, being largely dropped in favour of more lavish settings (epitomised by the re-imagining of Poirot's home as a larger, more lavish apartment). The series logo was redesigned (the full opening title sequence had not been used since series 6 in 1996), and the main theme motif, though used often, was usually featured subtly and in sombre arrangements; this has been described as a consequence of the novels adapted being darker and more psychologically driven. However, a more upbeat string arrangement of the theme music is used for the end credits of "Hallowe'en Party", "The Clocks" and "Dead Man's Folly". In flashback scenes, later episodes also made extensive use of fisheye lens, distorted colours, and other visual effects.


title: Agatha Christie's Poirot

text: Series 9–12 lack Hugh Fraser, Philip Jackson and Pauline Moran, who had appeared in the previous series (excepting series 4, where Moran is absent). Series 10 (2006) introduced Zoë Wanamaker as the eccentric crime novelist Ariadne Oliver and David Yelland as Poirot's dependable valet, George — a character that had been introduced in the early "Poirot" novels but was left out of the early adaptations to develop the character of Miss Lemon. The introduction of Wanamaker and Yelland's characters and the absence of the other characters is generally consistent with the stories on which the scripts were based. Hugh Fraser and David Yelland returned for two episodes of the final series ("The Big Four" and "Curtain"), with Philip Jackson and Pauline Moran returning for the adaptation of "The Big Four". Zoë Wanamaker also returned for the adaptations of "Elephants Can Remember" and "Dead Man's Folly".


title: Agatha Christie's Poirot

text: Clive Exton adapted seven novels and fourteen short stories for the series, including "The ABC Murders" and "The Murder of Roger Ackroyd", which received mixed reviews from critics. Anthony Horowitz was another prolific writer for the series, adapting three novels and nine short stories, while Nick Dear adapted six novels. Comedian and novelist Mark Gatiss wrote three episodes and also guest-starred in the series, as have Peter Flannery and Kevin Elyot. Ian Hallard, who co-wrote the screenplay for "The Big Four" with Mark Gatiss, appears in the episode and also "Hallowe'en Party", which was scripted by Gatiss alone.


title: Agatha Christie's Poirot

text: Florin Court in Charterhouse Square, London, was used as Poirot's fictional London residence, Whitehaven Mansions. The final episode to be filmed was "Dead Man's Folly" in June 2013 on the Greenway Estate (which was Agatha Christie's home) broadcast on 30 October 2013. Most of the locations and buildings where the episodes were shot were given fictional names.


title: Agatha Christie's Poirot

text: Suchet was recommended for the part by Christie's family, who had seen him appear as Blott in the TV adaptation of Tom Sharpe's "Blott on the Landscape". Suchet, a method actor, said that he prepared for the part by reading all the "Poirot" novels and every short story, and copying out every piece of description about the character. Suchet told "The Strand Magazine": "What I did was, I had my file on one side of me and a pile of stories on the other side and day after day, week after week, I ploughed through most of Agatha Christie's novels about Hercule Poirot and wrote down characteristics until I had a file full of documentation of the character. And then it was my business not only to know what he was like, but to gradually become him. I had to become him before we started shooting".


title: Agatha Christie's Poirot

text: During the filming of the first series, Suchet almost left the production during an argument with a director, insisting that Poirot's odd mannerisms (in this case, putting a handkerchief down before sitting on a park bench) be featured; he later said "there's no question [Poirot's] obsessive-compulsive". According to many critics and enthusiasts, Suchet's characterisation is considered to be the most accurate interpretation of all the actors who have played Poirot, and the closest to the character in the books. In 2013, Suchet revealed that Christie's daughter Rosalind Hicks had told him she was sure Christie would have approved of his performance.


title: Agatha Christie's Poirot

text: In 2007, Suchet spoke of his desire to film the remaining stories in the canon and hoped to achieve this before his 65th birthday in May 2011. Despite speculation of cancellation early in 2011, the remaining books were ultimately adapted into a thirteenth series, adapted in 2013 into 5 episodes, from which "Curtain" aired last on 13 November. A 2013 television special, "Being Poirot", centred on Suchet's characterisation and his emotional final episode.


title: Agatha Christie's Poirot

text: Alongside recurring characters, the early series featured actors who later achieved greater fame, including Sean Pertwee ("The King of Clubs", 1989; "Dead Man's Folly", 2013), Joely Richardson ("The Dream", 1989), Polly Walker ("Peril at End House", 1990), Samantha Bond ("The Adventure of the Cheap Flat", 1990), Christopher Eccleston ("One, Two, Buckle My Shoe", 1992), Hermione Norris ("Jewel Robbery at The Grand Metropolitan", 1993), Damian Lewis ("Hickory Dickory Dock", 1995), Jamie Bamber ("The Murder of Roger Ackroyd", 2000), Russell Tovey ("Evil Under the Sun", 2001), Kelly Reilly ("Sad Cypress", 2003), Emily Blunt ("Death on the Nile", 2004), Alice Eve ("The Mystery of the Blue Train", 2005), Michael Fassbender ("After the Funeral", 2006), Aiden Gillen ("Five Little Pigs", 2003), Toby Jones and Jessica Chastain ("Murder on the Orient Express", 2010), and Tom Ellis ("Dead Man's Folly", 2013).


title: Agatha Christie's Poirot

text: Four Academy Award nominees have appeared in the series: Sarah Miles, Barbara Hershey, Elizabeth McGovern and Elliott Gould. Peter Capaldi, Jessica Chastain, Michael Fassbender, Lesley Manville and Vanessa Kirby went on to receive Academy Award nominations after appearing on the show. Several members of British thespian families appeared in episodes throughout the course of the series. James Fox appeared as Colonel Race in "Death on the Nile", and his older brother Edward Fox appeared as Gudgeon in "The Hollow". Three of the Cusack sisters each appeared in an episode: Niamh Cusack in "The King of Clubs", Sorcha Cusack in "Jewel Robbery at The Grand Metropolitan", and Sinéad Cusack in "Dead Man's Folly". Phyllida Law and her daughter Sophie Thompson appeared in "Hallowe'en Party". David Yelland appeared as Charles Laverton West in "Murder in the Mews" and as George for the remainder of the series from Series 10 onward, and his daughter Hannah Yelland appeared as Geraldine Marsh in "Lord Edgware Dies".


title: Agatha Christie's Poirot

text: Agatha Christie's grandson Mathew Prichard commented: "Personally, I regret very much that she [Agatha Christie] never saw David Suchet. I think that visually he is much the most convincing and perhaps he manages to convey to the viewer just enough of the irritation that we always associate with the perfectionist, to be convincing!"


title: Agatha Christie's Poirot

text: In 2008, the series was described by some critics as going "off piste", though not negatively, from its old format. It was praised for its new writers, more lavish productions, and a greater emphasis on the darker psychology of the novels. Significantly, it was noted for "Five Little Pigs" (adapted by Kevin Elyot) bringing out a homosexual subtext of the novel. Nominations for twenty BAFTAs were received between 1989 and 1991 for series 1–3.


title: Agatha Christie's Poirot

text: In Region 1, Acorn Media has the rights to series 1–6 and 11–12. Series 7–10 are distributed by A&E, a co-producer on several of them. In North America, series 1–11 are available on Netflix and Amazon Prime instant streaming service. In Region 4, Acorn Media (distributed by "Reel DVD") has begun releasing the series on DVD in Australia in complete season sets. To date, they have released the first 8 series of the show. Series 1–9 and 12 are available in Spain (Region 2) on Blu-ray with Spanish and English audio tracks. Dutch FilmWorks were reported to be the first company to release series 12, in 2010.


title: Agatha Christie's Poirot

text: Beginning in 2011, Acorn began issuing the series on Blu-ray discs. As of 4 November 2014, series 1 through 13 have all been issued on DVD and Blu-ray by Acorn. The A&E DVD releases of series 7 through 10 correspond to the A&E versions broadcast in America which were missing sections of the original video as originally broadcast in the United Kingdom. The Acorn releases of series 7 through 10 restore the missing video.


title: Agatha Christie's Poirot

text: Being Poirot is a 50-minute ITV television documentary (2013) in which David Suchet attempts to unravel the mysterious appeal of Hercule Poirot and how he portrayed him. It was broadcast in the United Kingdom on the same evening as the final episode, "Curtain".


title: Agatha Christie's Poirot

text: Suchet visits the Greenway Estate, Agatha Christie's summer home, recollecting how he met her daughter Rosalind Hicks and her husband Anthony Hicks for their approval before he began filming. He meets Christie's grandson Mathew Prichard who recounts how his grandmother found the character amongst Belgian refugees in Torquay. There's a visit to the permanent Poirot exhibition at Torquay Museum to which he presented the cane he used in the television series.


title: Agatha Christie's Poirot

text: Suchet acknowledges the first stage and film adaptations of the books with actors such as Charles Laughton on the London stage in "Alibi", an adaptation of "The Murder of Roger Ackroyd", in 1928. "Alibi" was filmed in 1931 with Austin Trevor but is now lost. The oldest surviving film portrayal from 1934 was "Lord Edgware Dies" again with Austin Trevor portraying Poirot. Suchet notes a conscious decision was made by the film company to portray Poirot without a moustache. Films featuring Albert Finney and Peter Ustinov are also featured. Suchet reveals that he read the books and wrote down 93 notes about the character that he went on to use in his portrayal. The descriptions in the books helped him discover the voice he would use, and the rapid mincing gait.


title: Agatha Christie's Poirot

text: Suchet also goes to Florin Court, a place that the production company chose to represent his home Whitehaven Mansions. There he meets first producer Brian Eastman, with whom he discusses the set that was built based on the flats, and Eastman's decision to fix the stories in 1936. Suchet also visits composer Christopher Gunning who had composed four themes for Eastman, the first being Gunning's favourite. Eastman chose the fourth after having Gunning darken the tone.


title: Agatha Christie's Poirot

text: Suchet travels to Brussels, where he is feted by the police chief and mayor. He then goes to Ellezelles, which claims to be the birthplace of Poirot, and he is shown a birth certificate as proof. It says the date was 1 April, "April Fools' Day" (no year mentioned). Finally, Suchet travels on the Orient Express and recounts filming the episode "Dead Man's Folly" last at Greenway to finish on a high note.


title: Agatha Christie's Poirot

text: Suchet was proud to have completed the entire Poirot canon by the time of the broadcast of the final episode, only slightly short of the target he had set himself (in a 2007 interview) of completing the entire canon before his 65th birthday.


title: Agatha Christie's Poirot

text: The short stories and novellas "The Submarine Plans", "The Market Basing Mystery", "Christmas Adventure", "The Mystery of the Baghdad Chest", "The Second Gong", "The Incident of the Dog's Ball", and "Hercule Poirot and the Greenshore Folly" were not filmed in their original short story format, as Agatha Christie later rewrote these stories as novellas or novels ("The Incredible Theft", "Murder in the Mews", "The Adventure of the Christmas Pudding", "The Mystery of the Spanish Chest", "Dead Man's Mirror", "Dumb Witness", and "Dead Man's Folly" respectively) which were made into episodes.


title: Agatha Christie's Poirot

text: Unlike the other Poirot short story collections, where each story was adapted into a 1-hour episode, the collection entitled "The Labours of Hercules" (consisting of twelve short stories linked by an initial scene-setting story and a broad running theme) was adapted into a single 2-hour film. The end result drew heavily on some of the stories; other stories contributed only minor details. The original version of "The Capture of Cerberus", unpublished until 2009, was not used at all. Also incorporated into this single film was a character with the surname Lemesurier, as a nod to the short story "The Lemesurier Inheritance", which has otherwise not been included in the Poirot series.


title: Agatha Christie's Poirot

text: One other short story, "The Regatta Mystery", is not included in the Suchet series, as it is not generally considered part of the Poirot canon. First published in issue 546 of the "Strand Magazine" in June 1936 under the title "Poirot and the Regatta Mystery" (and illustrated by Jack M. Faulks), the story was later rewritten by Christie to change the detective from Hercule Poirot to Parker Pyne. It was as a Parker Pyne mystery that the story was first published in book format in "The Regatta Mystery and Other Stories" (published in the United States in 1939). Although the story is now associated with Parker Pyne, it was included in the 2008 omnibus volume "Hercule Poirot: the Complete Short Stories", which was the first public association of the story with Hercule Poirot since the original Strand Magazine publication of 1936.


title: Agatha Christie's Poirot

text: Aside from "Poirot and the Regatta Mystery", the one authentic Hercule Poirot story not included in any form, whole or partial, in the "Agatha Christie's Poirot" series is the 1930 play "Black Coffee". Although it was adapted into a novel in 1998, with the permission of the Christie Estate, it was not previously available in novel format. David Suchet did give a live reading of the original play version for the Agatha Christie Theatre Company and therefore felt that he had done justice to the entire authentic canon.


title: Franks

text: The Franks ( or ) were a group of Germanic peoples whose name was first mentioned in 3rd-century Roman sources, and associated with tribes between the Lower Rhine and the Ems River, on the edge of the Roman Empire. Later the term was associated with Romanized Germanic dynasties within the collapsing Western Roman Empire, who eventually commanded the whole region between the rivers Loire and Rhine. They imposed power over many other post-Roman kingdoms and Germanic peoples. Beginning with Charlemagne in 800, Frankish rulers were given recognition by the Catholic Church as successors to the old rulers of the Western Roman Empire.


title: Franks

text: Although the Frankish name does not appear until the 3rd century, at least some of the original Frankish tribes had long been known to the Romans under their own names, both as allies providing soldiers, and as enemies. The new name first appears when the Romans and their allies were losing control of the Rhine region. The Franks were first reported as working together to raid Roman territory. However, from the beginning, the Franks also suffered attacks upon them from outside their frontier area, by the Saxons, for example, and as frontier tribes they desired to move into Roman territory, with which they had centuries of close contact.


title: Franks

text: The Germanic tribes which formed the Frankish federation in Late Antiquity are associated with the Weser-Rhine Germanic/Istvaeonic cultural-linguistic grouping.


title: Franks

text: Frankish peoples inside Rome's frontier on the Rhine river included the Salian Franks who from their first appearance were permitted to live in Roman territory, and the Ripuarian or Rhineland Franks who, after many attempts, eventually conquered the Roman frontier city of Cologne and took control of the left bank of the Rhine. Later, in a period of factional conflict in the 450s and 460s, Childeric I, a Frank, was one of several military leaders commanding Roman forces with various ethnic affiliations in Roman Gaul (roughly modern France). Childeric and his son Clovis I faced competition from the Roman Aegidius as competitor for the "kingship" of the Franks associated with the Roman Loire forces (according to Gregory of Tours, Aegidius held the kingship of the Franks for 8 years while Childeric was in exile). This new type of kingship, perhaps inspired by Alaric I, represents the start of the Merovingian dynasty which succeeded in conquering most of Gaul in the 6th century, as well as establishing its leadership over all the Frankish kingdoms on the Rhine frontier. It was on the basis of this Merovingian empire that the resurgent Carolingians eventually came to be seen as the new Emperors of Western Europe in 800.


title: Franks

text: The terms "Frank" or "Frankish" subsequently developed several different levels, sometimes representing a very large part of Europe, and on the other hand sometimes limited to France. In the High and Late Middle Ages, Western Europeans shared their allegiance to the Catholic Church and worked as allies in the Crusades beyond Europe in the Levant. In 1099, the crusader population of Jerusalem mostly comprised French settlers who, at the time, were still referred to as Franks, and other Europeans such as Spaniards, Germans, and Hungarians. French knights made up the bulk of the steady flow of reinforcements throughout the two-hundred-year span of the Crusades, in such a fashion that the Arabs uniformly continued to refer to the crusaders and West Europeans as "Franjī" caring little whether they really came from France. The French Crusaders also imported the French language into the Levant, making French the base of the "lingua franca" (lit. "Frankish language") of the Crusader states. This has had a lasting impact on names for Western Europeans in many languages. Western Europe is known alternatively as "Frangistan" to the Persians.


title: Franks

text: Following the Treaty of Verdun in 843, the Frankish Realm was divided into three separate kingdoms: West Francia, Middle Francia, and East Francia. In 870, Middle Francia was partitioned again, with most of its territory being divided among West and East Francia, which would hence form the nuclei of the future Kingdom of France and the Holy Roman Empire respectively, with West Francia (France) eventually retaining the choronym.


title: Franks

text: The name was not a tribal name, but within a few centuries it had eclipsed the names of the original peoples who constituted them. Following the precedents of Edward Gibbon and Jacob Grimm, the name of the Franks has been linked with the English adjective "frank", originally meaning "free". There have also been proposals that Frank comes from the Germanic word for "javelin" (such as in Old English or Old Norse ). Words in other Germanic languages meaning "fierce", "bold" or "insolent" (German , Middle Dutch , Old English and Old Norwegian ), may also be significant.


title: Franks

text: Eumenius addressed the Franks in the matter of the execution of Frankish prisoners in the circus at Trier by Constantine I in 306 and certain other measures: ("Where now is that ferocity of yours? Where is that ever untrustworthy fickleness?"). Latin was used often to describe the Franks. Contemporary definitions of Frankish ethnicity vary both by period and point of view. The formulary of Marculf written about 700 AD described a continuation of national identities within a mixed population when it stated that "all the peoples who dwell (in the official's province), Franks, Romans, Burgundians and those of other nations, live … according to their law and their custom." Writing in 2009, Professor Christopher Wickham pointed out that "the word 'Frankish' quickly ceased to have an exclusive ethnic connotation. North of the River Loire everyone seems to have been considered a Frank by the mid-7th century at the latest (except Bretons); "Romani" (Romans) were essentially the inhabitants of Aquitaine after that".


title: Franks

text: Apart from the "History of the Franks" by Gregory of Tours, two early sources relate the mythological origin of the Franks: a 7th-century work known as the "Chronicle of Fredegar" and the anonymous , written a century later.


title: Franks

text: The author of the "Chronicle of Fredegar" claimed that the Franks came originally from Troy and quoted the works of Virgil and Hieronymus:


title: Franks

text: According to historian Patrick J. Geary, those two stories are "alike in betraying both the fact that the Franks knew little about their background and that they may have felt some inferiority in comparison with other peoples of antiquity who possessed an ancient name and glorious tradition. (...) Both legends are of course equally fabulous for, even more than most barbarian peoples, the Franks possessed no common history, ancestry, or tradition of a heroic age of migration. Like their Alemannic neighbours, they were by the sixth century a fairly recent creation, a coalition of Rhenish tribal groups who long maintained separate identities and institutions."


title: Franks

text: The other work, the , previously known as before its republication in 1888 by Bruno Krusch, described how 12,000 Trojans, led by Priam and Antenor, sailed from Troy to the River Don in Russia and on to Pannonia, which is on the River Danube, settling near the Sea of Azov. There they founded a city called Sicambria. (The Sicambri were the most well-known tribe in the Frankish homeland in the time of the early Roman empire, still remembered though defeated and dispersed long before the Frankish name appeared.) The Trojans joined the Roman army in accomplishing the task of driving their enemies into the marshes of Mæotis, for which they received the name of Franks (meaning "fierce"). A decade later the Romans killed Priam and drove away Marcomer and Sunno, the sons of Priam and Antenor, and the other Franks.


title: Franks

text: The major primary sources on the early Franks include the , Ammianus Marcellinus, Claudian, Zosimus, Sidonius Apollinaris and Gregory of Tours. The Franks are first mentioned in the "Augustan History", a collection of biographies of the Roman emperors. None of these sources presents a detailed list of which tribes or parts of tribes became Frankish, or concerning the politics and history, but to quote :


title: Franks

text: The Franks were described in Roman texts both as allies () and enemies (). About the year 260 one group of Franks penetrated as far as Tarragona in present-day Spain, where they plagued the region for about a decade before they were subdued and expelled by the Romans. In 287 or 288, the Roman Caesar Maximian forced a Frankish leader Genobaud and his people to surrender without a fight.


title: Franks

text: In 288 the emperor Maximian defeated the Salian Franks, Chamavi, Frisii and other Germanic people living along the Rhine and moved them to Germania inferior to provide manpower and prevent the settlement of other Germanic tribes. In 292 Constantius, the father of Constantine I defeated the Franks who had settled at the mouth of the Rhine. These were moved to the nearby region of Toxandria. Eumenius mentions Constantius as having "killed, expelled, captured [and] kidnapped" the Franks who had settled there and others who had crossed the Rhine, using the term for the first time. It seems likely that the term Frank in this first period had a broader meaning, sometimes including coastal Frisii.


title: Franks

text: The "Life of Aurelian", which was possibly written by Vopiscus, mentions that in 328, Frankish raiders were captured by the 6th Legion stationed at Mainz. As a result of this incident, 700 Franks were killed and 300 were sold into slavery. Frankish incursions over the Rhine became so frequent that the Romans began to settle the Franks on their borders in order to control them.


title: Franks

text: The Franks are mentioned in the , an atlas of Roman roads. It is a 13th-century copy of a 4th or 5th century document that reflects information from the 3rd century. The Romans knew the shape of Europe, but their knowledge is not evident from the map, which was only a practical guide to the roads to be followed from point to point. In the middle Rhine region of the map, the word Francia is close to a misspelling of Bructeri. Beyond Mainz is Suevia, the country of the Suebi, and beyond that is Alamannia, the country of the Alamanni. Four tribes at the mouth of the Rhine are depicted: the Chauci, the Amsivarii ('Ems dwellers'), the Cherusci and the Chamavi, followed by ('who are also Franks'). This implies that the Chamavi were considered Franks. The "Tabula" was probably based on the , a map of twenty years' labour commissioned by Augustus and then kept by the Roman's treasury department for the assessment of taxes. It did not survive as such. Information about the imperial divisions of Gaul probably derives from it.


title: Franks

text: The Salians were first mentioned by Ammianus Marcellinus, who described Julian's defeat of "the first Franks of all, those whom custom has called the Salians," in 358. Julian allowed the Franks to remain in Texuandria as within the Empire, having moved there from the Rhine-Maas delta. The 5th century lists a group of soldiers as .


title: Franks

text: Some decades later, Franks in the same region, possibly the Salians, controlled the River Scheldt and were disrupting transport links to Britain in the English Channel. Although Roman forces managed to pacify them, they failed to expel the Franks, who continued to be feared as pirates.


title: Franks

text: The Salians are generally seen as the predecessors of the Franks who pushed southwestwards into what is now modern France, who eventually came to be ruled by the Merovingians (see below). This is because when the Merovingian dynasty published the Salian law ("Lex Salica") it applied in the Neustrian area from the river Liger (Loire) to the "Silva Carbonaria", the western kingdom founded by them outside the original area of Frankish settlement. In the 5th century, Franks under Chlodio pushed into Roman lands in and beyond the ""Silva Carbonaria"" or "Charcoal forest", which ran through the area of modern western Wallonia. The forest was the boundary of the original Salian territories to the north and the more Romanized area to the south in the Roman province of "Belgica Secunda" (roughly equivalent to what Julius Caesar had long ago called "Belgium"). Chlodio conquered Tournai, Artois, Cambrai, and as far as the Somme river. Chlodio is often seen as an ancestor of the future Merovingian dynasty. Childeric I, who according to Gregory of Tours was a reputed descendant of Chlodio, was later seen as administrative ruler over Roman "Belgica Secunda" and possibly other areas.


title: Franks

text: Records of Childeric show him to have been active together with Roman forces in the Loire region, quite far to the south. His descendants came to rule Roman Gaul all the way to there, and this became the Frankish kingdom of Neustria, the basis of what would become medieval France. Childeric's son Clovis I also took control of the more independent Frankish kingdoms east of the Silva Carbonaria and Belgica II. This later became the Frankish kingdom of Austrasia, where the early legal code was referred to as "Ripuarian".


title: Franks

text: The Rhineland Franks who lived near the stretch of the Rhine from roughly Mainz to Duisburg, the region of the city of Cologne, are often considered separately from the Salians, and sometimes in modern texts referred to as Ripuarian Franks. The Ravenna Cosmography suggests that "Francia Renensis" included the old "civitas" of the Ubii, in Germania II (Germania Inferior), but also the northern part of Germania I (Germania Superior), including Mainz. Like the Salians they appear in Roman records both as raiders and as contributors to military units. Unlike the Salii, there is no record of when, if ever, the empire officially accepted their residence within its borders. They eventually succeeded to hold the city of Cologne, and at some point seem to have acquired the name Ripuarians, which may have meant "river people". In any case a Merovingian legal code was called the "Lex Ribuaria", but it probably applied in all the older Frankish lands, including the original Salian areas.


title: Franks

text: Jordanes, in "Getica" mentions the Riparii as auxiliaries of Flavius Aetius during the Battle of Châlons in 451: But these ("river dwellers") are today not considered to be Ripuarian Franks, but a known military unit based on the river Rhone.


title: Franks

text: Their territory on both sides of the Rhine became a central part of Merovingian Austrasia, which stretched to include Roman Germania Inferior (later "Germania Secunda", which included the original Salian and Ripuarian lands, and roughly equates to medieval Lower Lotharingia) as well as Gallia Belgica Prima (late Roman "Belgium", roughly medieval Upper Lotharingia), and lands on the east bank of the Rhine.


title: Franks

text: Gregory of Tours (Book II) reported that small Frankish kingdoms existed during the fifth century around Cologne, Tournai, Cambrai and elsewhere. The kingdom of the Merovingians eventually came to dominate the others, possibly because of its association with Roman power structures in northern Gaul, into which the Frankish military forces were apparently integrated to some extent. Aegidius, was originally the of northern Gaul appointed by Majorian, but after Majorian's death apparently seen as a Roman rebel who relied on Frankish forces. Gregory of Tours reported that Childeric I was exiled for 8 years while Aegidius held the title of "King of the Franks". Eventually Childeric returned and took the same title. Aegidius died in 464 or 465. Childeric and his son Clovis I were both described as rulers of the Roman Province of , by its spiritual leader in the time of Clovis, Saint Remigius.


title: Franks

text: Clovis later defeated the son of Aegidius, Syagrius, in 486 or 487 and then had the Frankish king Chararic imprisoned and executed. A few years later, he killed Ragnachar, the Frankish king of Cambrai, and his brothers. After conquering the Kingdom of Soissons and expelling the Visigoths from southern Gaul at the Battle of Vouillé, he established Frankish hegemony over most of Gaul, excluding Burgundy, Provence and Brittany, which were eventually absorbed by his successors. By the 490s, he had conquered all the Frankish kingdoms to the west of the River Maas except for the Ripuarian Franks and was in a position to make the city of Paris his capital. He became the first king of all Franks in 509, after he had conquered Cologne.


title: Franks

text: Clovis I divided his realm between his four sons, who united to defeat Burgundy in 534. Internecine feuding occurred during the reigns of the brothers Sigebert I and Chilperic I, which was largely fuelled by the rivalry of their queens, Brunhilda and Fredegunda, and which continued during the reigns of their sons and their grandsons. Three distinct subkingdoms emerged: Austrasia, Neustria and Burgundy, each of which developed independently and sought to exert influence over the others. The influence of the Arnulfing clan of Austrasia ensured that the political centre of gravity in the kingdom gradually shifted eastwards to the Rhineland.


title: Franks

text: The Frankish realm was reunited in 613 by Chlothar II, the son of Chilperic, who granted his nobles the Edict of Paris in an effort to reduce corruption and reassert his authority. Following the military successes of his son and successor Dagobert I, royal authority rapidly declined under a series of kings, traditionally known as "les rois fainéants". After the Battle of Tertry in 687, each mayor of the palace, who had formerly been the king's chief household official, effectively held power until in 751, with the approval of the Pope and the nobility, Pepin the Short deposed the last Merovingian king Childeric III and had himself crowned. This inaugurated a new dynasty, the Carolingians.


title: Franks

text: The unification achieved by the Merovingians ensured the continuation of what has become known as the Carolingian Renaissance. The Carolingian Empire was beset by internecine warfare, but the combination of Frankish rule and Roman Christianity ensured that it was fundamentally united. Frankish government and culture depended very much upon each ruler and his aims and so each region of the empire developed differently. Although a ruler's aims depended upon the political alliances of his family, the leading families of Francia shared the same basic beliefs and ideas of government, which had both Roman and Germanic roots.


title: Franks

text: The Frankish state consolidated its hold over the majority of western Europe by the end of the 8th century, developing into the Carolingian Empire. With the coronation of their ruler Charlemagne as Holy Roman Emperor by Pope Leo III in 800 AD, he and his successors were recognised as legitimate successors to the emperors of the Western Roman Empire. As such, the Carolingian Empire gradually came to be seen in the West as a continuation of the ancient Roman Empire. This empire would give rise to several successor states, including France, the Holy Roman Empire and Burgundy, though the "Frankish" identity remained most closely identified with France.


title: Franks

text: After the death of Charlemagne, his only adult surviving son became Emperor and King Louis the Pious. Following Louis the Pious's death, however, according to Frankish culture and law that demanded equality among all living male adult heirs, the Frankish Empire was now split between Louis' three sons.


title: Franks

text: Germanic peoples, including those tribes in the Rhine delta that later became the Franks, are known to have served in the Roman army since the days of Julius Caesar. After the Roman administration collapsed in Gaul in the 260s, the armies under the Germanic Batavian Postumus revolted and proclaimed him emperor and then restored order. From then on, Germanic soldiers in the Roman army, most notably Franks, were promoted from the ranks. A few decades later, the Menapian Carausius created a Batavian–British rump state on Roman soil that was supported by Frankish soldiers and raiders. Frankish soldiers such as Magnentius, Silvanus and Arbitio held command positions in the Roman army during the mid 4th century. From the narrative of Ammianus Marcellinus it is evident that both Frankish and Alamannic tribal armies were organised along Roman lines.


title: Franks

text: After the invasion of Chlodio, the Roman armies at the Rhine border became a Frankish "franchise" and Franks were known to levy Roman-like troops that were supported by a Roman-like armour and weapons industry. This lasted at least until the days of the scholar Procopius (c. 500 – c. 565), more than a century after the demise of the Western Roman Empire, who wrote describing the former "Arborychoi", having merged with the Franks, retaining their legionary organization in the style of their forefathers during Roman times. The Franks under the Merovingians melded Germanic custom with Romanised organisation and several important tactical innovations. Before their conquest of Gaul, the Franks fought primarily as a tribe, unless they were part of a Roman military unit fighting in conjunction with other imperial units.


title: Franks

text: The primary sources for Frankish military custom and armament are Ammianus Marcellinus, Agathias and Procopius, the latter two Eastern Roman historians writing about Frankish intervention in the Gothic War.


title: Franks

text: In the "Strategikon", supposedly written by the emperor Maurice, or in his time, the Franks are lumped together with the Lombards under the heading of the "fair-haired" peoples.


title: Franks

text: While the above quotations have been used as a statement of the military practices of the Frankish nation in the 6th century and have even been extrapolated to the entire period preceding Charles Martel's reforms (early mid-8th century), post-Second World War historiography has emphasised the inherited Roman characteristics of the Frankish military from the date of the beginning of the conquest of Gaul. The Byzantine authors present several contradictions and difficulties. Procopius denies the Franks the use of the spear while Agathias makes it one of their primary weapons. They agree that the Franks were primarily infantrymen, threw axes and carried a sword and shield. Both writers also contradict the authority of Gallic authors of the same general time period (Sidonius Apollinaris and Gregory of Tours) and the archaeological evidence. The , the early 7th century legal code of the Rhineland or Ripuarian Franks, specifies the values of various goods when paying a wergild in kind; whereas a spear and shield were worth only two , a sword and scabbard were valued at seven, a helmet at six, and a "metal tunic" at twelve. Scramasaxes and arrowheads are numerous in Frankish graves even though the Byzantine historians do not assign them to the Franks.


title: Franks

text: The evidence of Gregory and of the implies that the early Franks were a cavalry people. In fact, some modern historians have hypothesised that the Franks possessed so numerous a body of horses that they could use them to plough fields and thus were agriculturally technologically advanced over their neighbours. The specifies that a mare's value was the same as that of an ox or of a shield and spear, two and a stallion seven or the same as a sword and scabbard, which suggests that horses were relatively common. Perhaps the Byzantine writers considered the Frankish horse to be insignificant relative to the Greek cavalry, which is probably accurate.


title: Franks

text: The Frankish military establishment incorporated many of the pre-existing Roman institutions in Gaul, especially during and after the conquests of Clovis I in the late 5th and early 6th centuries. Frankish military strategy revolved around the holding and taking of fortified centres () and in general these centres were held by garrisons of or , who were former Roman mercenaries of Germanic origin. Throughout Gaul, the descendants of Roman soldiers continued to wear their uniforms and perform their ceremonial duties.


title: Franks

text: Immediately beneath the Frankish king in the military hierarchy were the , his sworn followers, who were generally 'old soldiers' in service away from court. The king had an elite bodyguard called the "truste". Members of the "truste" often served in , garrison settlements that were established for military and police purposes. The day-to-day bodyguard of the king was made up of "antrustiones" (senior soldiers who were aristocrats in military service) and (junior soldiers and not aristocrats). All high-ranking men had "pueri".


title: Franks

text: The Frankish military was not composed solely of Franks and Gallo-Romans, but also contained Saxons, Alans, Taifals and Alemanni. After the conquest of Burgundy (534), the well-organised military institutions of that kingdom were integrated into the Frankish realm. Chief among these was the standing army under the command of the Patrician of Burgundy.


title: Franks

text: In the late 6th century, during the wars instigated by Fredegund and Brunhilda, the Merovingian monarchs introduced a new element into their militaries: the local levy. A levy consisted of all the able-bodied men of a district who were required to report for military service when called upon, similar to conscription. The local levy applied only to a city and its environs. Initially only in certain cities in western Gaul, in Neustria and Aquitaine, did the kings possess the right or power to call up the levy. The commanders of the local levies were always different from the commanders of the urban garrisons. Often the former were commanded by the counts of the districts. A much rarer occurrence was the general levy, which applied to the entire kingdom and included peasants ( and ). General levies could also be made within the still-pagan trans-Rhenish stem duchies on the orders of a monarch. The Saxons, Alemanni and Thuringii all had the institution of the levy and the Frankish monarchs could depend upon their levies until the mid-7th century, when the stem dukes began to sever their ties to the monarchy. Radulf of Thuringia called up the levy for a war against Sigebert III in 640.


title: Franks

text: Soon the local levy spread to Austrasia and the less Romanised regions of Gaul. On an intermediate level, the kings began calling up territorial levies from the regions of Austrasia (which did not have major cities of Roman origin). All the forms of the levy gradually disappeared, however, in the course of the 7th century after the reign of Dagobert I. Under the so-called , the levies disappeared by mid-century in Austrasia and later in Burgundy and Neustria. Only in Aquitaine, which was fast becoming independent of the central Frankish monarchy, did complex military institutions persist into the 8th century. In the final half of the 7th century and first half of the 8th in Merovingian Gaul, the chief military actors became the lay and ecclesiastical magnates with their bands of armed followers called retainers. The other aspects of the Merovingian military, mostly Roman in origin or innovations of powerful kings, disappeared from the scene by the 8th century.


title: Franks

text: Merovingian armies used coats of mail, helmets, shields, lances, swords, bows and arrows and war horses. The armament of private armies resembled those of the Gallo-Roman of the late Empire. A strong element of Alanic cavalry settled in Armorica influenced the fighting style of the Bretons down into the 12th century. Local urban levies could be reasonably well-armed and even mounted, but the more general levies were composed of and , who were mostly farmers by trade and carried ineffective weapons, such as farming implements. The peoples east of the Rhine – Franks, Saxons and even Wends – who were sometimes called upon to serve, wore rudimentary armour and carried weapons such as spears and axes. Few of these men were mounted.


title: Franks

text: Merovingian society had a militarised nature. The Franks called annual meetings every Marchfeld (1 March), when the king and his nobles assembled in large open fields and determined their targets for the next campaigning season. The meetings were a show of strength on behalf of the monarch and a way for him to retain loyalty among his troops. In their civil wars, the Merovingian kings concentrated on the holding of fortified places and the use of siege engines. In wars waged against external foes, the objective was typically the acquisition of booty or the enforcement of tribute. Only in the lands beyond the Rhine did the Merovingians seek to extend political control over their neighbours.


title: Franks

text: Tactically, the Merovingians borrowed heavily from the Romans, especially regarding siege warfare. Their battle tactics were highly flexible and were designed to meet the specific circumstances of a battle. The tactic of subterfuge was employed endlessly. Cavalry formed a large segment of an army , but troops readily dismounted to fight on foot. The Merovingians were capable of raising naval forces: the naval campaign waged against the Danes by Theuderic I in 515 involved ocean-worthy ships and rivercraft were used on the Loire, Rhône and Rhine.


title: Franks

text: In a modern linguistic context, the language of the early Franks is variously called "Old Frankish" or "Old Franconian" and these terms refer to the language of the Franks prior to the advent of the High German consonant shift, which took place between 600 and 700 CE. After this consonant shift the Frankish dialect diverges, with the dialects which would become modern Dutch not undergoing the consonantal shift, while all others did so to varying degrees. As a result, the distinction between Old Dutch and Old Frankish is largely negligible, with Old Dutch (also called Old Low Franconian) being the term used to differentiate between the affected and non-affected variants following the aforementioned Second Germanic consonant shift.


title: Franks

text: The Frankish language has not been directly attested, apart from a very small number of runic inscriptions found within contemporary Frankish territory such as the Bergakker inscription. Nevertheless a significant amount of Frankish vocabulary has been reconstructed by examining early Germanic loanwords found in Old French as well as through comparative reconstruction through Dutch. The influence of Old Frankish on contemporary Gallo-Roman vocabulary and phonology, have long been questions of scholarly debate. Frankish influence is thought to include the designations of the four cardinal directions: "nord" "north", "sud" "south", "est" "east" and "ouest" "west" and at least an additional 1000 stem words.


title: Franks

text: Although the Franks would eventually conquer all of Gaul, speakers of Frankish apparently expanded in sufficient numbers only into northern Gaul to have a linguistic effect. For several centuries, northern Gaul was a bilingual territory (Vulgar Latin and Frankish). The language used in writing, in government and by the Church was Latin. Urban T. Holmes has proposed that a Germanic language continued to be spoken as a second tongue by public officials in western Austrasia and Northern Neustria as late as the 850s, and that it completely disappeared as a spoken language during the 10th century from regions where only French is spoken today.


title: Franks

text: Early Frankish art and architecture belongs to a phase known as Migration Period art, which has left very few remains. The later period is called Carolingian art, or, especially in architecture, pre-Romanesque. Very little Merovingian architecture has been preserved. The earliest churches seem to have been timber-built, with larger examples being of a basilica type. The most completely surviving example, a baptistery in Poitiers, is a building with three apses of a Gallo-Roman style. A number of small baptistries can be seen in Southern France: as these fell out of fashion, they were not updated and have subsequently survived as they were.


title: Franks

text: Jewelry (such as brooches), weapons (including swords with decorative hilts) and clothing (such as capes and sandals) have been found in a number of grave sites. The grave of Queen Aregund, discovered in 1959, and the Treasure of Gourdon, which was deposited soon after 524, are notable examples. The few Merovingian illuminated manuscripts that have survived, such as the Gelasian Sacramentary, contain a great deal of zoomorphic representations. Such Frankish objects show a greater use of the style and motifs of Late Antiquity and a lesser degree of skill and sophistication in design and manufacture than comparable works from the British Isles. So little has survived, however, that the best quality of work from this period may not be represented.


title: Franks

text: The objects produced by the main centres of the Carolingian Renaissance, which represent a transformation from that of the earlier period, have survived in far greater quantity. The arts were lavishly funded and encouraged by Charlemagne, using imported artists where necessary, and Carolingian developments were decisive for the future course of Western art. Carolingian illuminated manuscripts and ivory plaques, which have survived in reasonable numbers, approached those of Constantinople in quality. The main surviving monument of Carolingian architecture is the Palatine Chapel in Aachen, which is an impressive and confident adaptation of San Vitale, Ravenna – from where some of the pillars were brought. Many other important buildings existed, such as the monasteries of Centula or St Gall, or the old Cologne Cathedral, since rebuilt. These large structures and complexes made frequent use of towers.


title: Franks

text: A sizeable portion of the Frankish aristocracy quickly followed Clovis in converting to Christianity (the Frankish church of the Merovingians). The conversion of all under Frankish rule required a considerable amount of time and effort.


title: Franks

text: Echoes of Frankish paganism can be found in the primary sources, but their meaning is not always clear. Interpretations by modern scholars differ greatly, but it is likely that Frankish paganism shared most of the characteristics of other varieties of Germanic paganism. The mythology of the Franks was probably a form of Germanic polytheism. It was highly ritualistic. Many daily activities centred around the multiple deities, chiefest of which may have been the Quinotaur, a water-god from whom the Merovingians were reputed to have derived their ancestry. Most of their gods were linked with local cult centres and their sacred character and power were associated with specific regions, outside of which they were neither worshipped nor feared. Most of the gods were "worldly", possessing form and having connections with specific objects, in contrast to the God of Christianity.


title: Franks

text: Frankish paganism has been observed in the burial site of Childeric I, where the king's body was found covered in a cloth decorated with numerous bees. There is a likely connection with the bees to the traditional Frankish weapon, the angon (meaning "sting"), from its distinctive spearhead. It is possible that the fleur-de-lis is derived from the angon.


title: Franks

text: Some Franks, like the 4th century usurper Silvanus, converted early to Christianity. In 496, Clovis I, who had married a Burgundian Catholic named Clotilda in 493, was baptised by Saint Remi after a decisive victory over the Alemanni at the Battle of Tolbiac. According to Gregory of Tours, over three thousand of his soldiers were baptised with him. Clovis' conversion had a profound effect on the course of European history, for at the time the Franks were the only major Christianised Germanic tribe without a predominantly Arian aristocracy and this led to a naturally amicable relationship between the Catholic Church and the increasingly powerful Franks.


title: Franks

text: Although many of the Frankish aristocracy quickly followed Clovis in converting to Christianity, the conversion of all his subjects was only achieved after considerable effort and, in some regions, a period of over two centuries. The "Chronicle of St. Denis" relates that, following Clovis' conversion, a number of pagans who were unhappy with this turn of events rallied around Ragnachar, who had played an important role in Clovis' initial rise to power. Although the text remains unclear as to the precise pretext, Clovis had Ragnachar executed. Remaining pockets of resistance were overcome region by region, primarily due to the work of an expanding network of monasteries.


title: Franks

text: The Merovingian Church was shaped by both internal and external forces. It had to come to terms with an established Gallo-Roman hierarchy that resisted changes to its culture, Christianise pagan sensibilities and suppress their expression, provide a new theological basis for Merovingian forms of kingship deeply rooted in pagan Germanic tradition and accommodate Irish and Anglo-Saxon missionary activities and papal requirements. The Carolingian reformation of monasticism and church-state relations was the culmination of the Frankish Church.


title: Franks

text: The increasingly wealthy Merovingian elite endowed many monasteries, including that of the Irish missionary Columbanus. The 5th, 6th and 7th centuries saw two major waves of hermitism in the Frankish world, which led to legislation requiring that all monks and hermits follow the Rule of St Benedict. The Church sometimes had an uneasy relationship with the Merovingian kings, whose claim to rule depended on a mystique of royal descent and who tended to revert to the polygamy of their pagan ancestors. Rome encouraged the Franks to slowly replace the Gallican Rite with the Roman rite. When the mayors took over, the Church was supportive and an Emperor crowned by the Pope was much more to their liking.