memory function versus binary correlator in additive markov chains abstract we study properties of the additive binary markov chain with short and long range correlations a new approach is suggested that allows one to express global statistical properties of a binary chain in terms of the so called memory function the latter is directly connected with the pair correlator of a chain via the integral equation that is analyzed in great detail to elucidate the relation between the memory function and pair correlator some specific cases were considered that may have important applications in different fields

conical zeta values and their double subdivision relations abstract we introduce the concept of a conical zeta value as a geometric generalization of a multiple zeta value in the context of convex cones the quasi shuffle and shuffle relations of multiple zeta values are generalized to open cone subdivision and closed cone subdivision relations respectively for conical zeta values in order to achieve the closed cone subdivision relation we also interpret linear relations among fractions as subdivisions of decorated closed cones as a generalization of the double shuffle relation of multiple zeta values we give the double subdivision relation of conical zeta values and formulate the extended double subdivision relation conjecture for conical zeta values

special values of multiple polylogarithms historically the polylogarithm has attracted specialists and non specialists alike with its lovely evaluations much the same can be said for euler sums or multiple harmonic sums which within the past decade have arisen in combinatorics knot theory and high energy physics more recently we have been forced to consider multidimensional extensions encompassing the classical polylogarithm euler sums and the riemann zeta function here we provide a general framework within which previously isolated results can now be properly understood applying the theory developed herein we prove several previously conjectured evaluations including an intriguing conjecture of don zagier

phase field simulations of interfacial dynamics in viscoelastic fluids using finite elements with adaptive meshing this paper describes a novel numerical algorithm for simulating interfacial dynamics of non newtonian fluids the interface between two immiscible fluids is treated as a thin mixing layer across which physical properties vary steeply but continuously the property and evolution of the interfacial layer is governed by a phase field variable that obeys a cahn hilliard type of convection diffusion equation this circumvents the task of directly tracking the interface and produces the correct interfacial tension from the free energy stored in the mixing layer viscoelasticity and other types of constitutive equations can be incorporated easily into the variational phase field framework the greatest challenge of this approach is in resolving the sharp gradients at the interface this is achieved by using an efficient adaptive meshing scheme governed by the phase field variable the finite element scheme easily accommodates complex flow geometry and the adaptive meshing makes it possible to simulate large scale two phase systems of complex fluids in two dimensional and axisymmetric three dimensional implementations the numerical toolkit is applied here to drop deformation in shear and elongational flows rise of drops and retraction of drops and torii some of these solutions serve as validation of the method and illustrate its key features while others explore novel physics of viscoelasticity in the deformation and evolution of interfaces

the algebra of multiple harmonic series abstract recently there has been much interest in multiple harmonic series i 1 i 2 i k n 1 n 2 n k 1 1 n 1 i 1 n 2 i 2 n k i k which converge when the exponentsijare positive integers andi1 1 also known as multiple zeta values or euler zagier sums starting with the noncommutative polynomial algebraq x y we define a second multiplication which is commutative and associative and call the resulting structure the harmonic algebra h as a graded commutative algebra h turns out to be a free polynomial algebra with the number of generators in degreengiven by the witt formula for the numbern n of basis elements of degreenin the free lie algebra on two generators multiple harmonic series can be thought of as images under a map h 0 rwhich is a homomorphism with respect to the commutative multiplication where h 0is an appropriate subalgebra of h if we calli1 ikthe weight of the series i1 ik then forn 1 there are at mostn n series of weightnthat are irreducible in the sense that they are not sums of rational multiples of products of multiple harmonic series of lower weight in fact our approach gives an explicit set of algebraically irreducible multiple harmonic series we also show that there is a subalgebra h 0 h 1 h related to the shuffle algebra which contains the algebra s of symmetric functions in fact maps the elements of s h 0to algebraic combinations of zeta values i for integeri 2 the map is not injective we show how several results about multiple harmonic series can be recast as statements about the kernel of and propose some conjectures on the structure of the algebra h 0 ker

kawashima s relations for interpolated multiple zeta values abstract recently yamamoto introduced polynomials in one variable t which interpolates multiple zeta and zeta star values t mzvs for short provided new prospects on two one conjecture of ohno and zudilin and proved the cyclic sum formula for t mzvs in this paper we establish a generalization of kawashima s relations t kawashima relations for t mzvs we prove the cyclic sum formula for t mzvs using a type of derivation operator together with the t kawashima relations

relations between elliptic multiple zeta values and a special derivation algebra we investigate relations between elliptic multiple zeta values and describe a method to derive the number of indecomposable elements of given weight and length our method is based on representing elliptic multiple zeta values as iterated integrals over eisenstein series and exploiting the connection with a special derivation algebra its commutator relations give rise to constraints on the iterated integrals over eisenstein series relevant for elliptic multiple zeta values and thereby allow to count the indecomposable representatives conversely the above connection suggests apparently new relations in the derivation algebra under https tools aei mpg de emzv we provide relations for elliptic multiple zeta values over a wide range of weights and lengths ar x iv 1 50 7 02 25 4v 1 he pth 8 j ul 2 01 5

local correlations in one and two dimensional disordered systems in one dimensional disordered systems all states are localized but when you add local correlations such as a dimer impurity some states become delocalized in this paper a wide range of correlations are studied leading to a delocalization of states moreover second nearest neighbour models which also have extended states are investigated finally a new approach to the case of two dimensions is presented using a matrix transfer technique where explicit extended states are found

alternating double euler sums hypergeometric identities and a theorem of zagier abstract in this work we derive relations between generating functions of double stuffle relations and double shuffle relations to express the alternating double euler sums r s r s and r s with r s odd in terms of zeta values we also give a direct proof of a hypergeometric identity which is a limiting case of a basic hypergeometric identity of andrews finally we gave another proof for the formula of zagier on the multiple zeta values 2 2 3 2 2

multivariable hoffman ihara operators and the operad of formal power series abstract we introduce a family of multilinear operators on a quasi shuffle algebra h which we call hoffman ihara operators it generalizes the linear operators constructed by hoffman and further studied by hoffman and ihara we prove the formula on the composition of these operators and show that this formula provides a unified and transparent understanding of some results on shuffle and quasi shuffle products an interpretation as an action of the operad of formal power series is also given

an alternative proof of a theorem of zagier abstract we give a new proof of zagier s theorem on evaluation of multiple zeta star values at 2 a 3 2 b the novelty of the proof consists in employing a hypergeometric identity of andrews which expresses a very well poised hypergeometric series in terms of a multiple series and the residue theorem

multiple q zeta values we introduce a q analog of the multiple harmonic series commonly referred to as multiple zeta values the multiple q zeta values satisfy a q stuffle multiplica tion rule analogous to the stuffle multiplication rule arising from the series representation of ordinary multiple zeta values additionally multiple q zeta values can be viewed as special values of the multiple q polylogarithm which admits a multiple jackson q integral representation whose limiting case is the drinfel d simplex integral for the ordinary multiple polylogarithm when q 1 the multiple jackson q integral representation for multiple q zeta values leads to a second multiplication rule satisfied by them referred to as a q shuffle despite this it appears that many numerical relations satisfied by ordinary multiple zeta values have no interesting q extension for example a suitable q analog of broadhurst s formula for 3 1 n if one exists is likely to be rather complicated nevertheless we show that a number of infinite classes of relations inc luding hoffman s partition identities ohno s cyclic sum identities granville s sum formula euler s convolution formula ohno s generalized duality relation and the derivation relations of ihara and kaneko extend to multiple q zeta values

guaranteed quality triangular mesh generation for domains with curved boundaries guaranteed quality unstructured meshing algorithms facilitate the development of automatic meshing tools however these algorithms require domains discretized using a set of linear segments leading to numerical errors in domains with curved boundaries we introduce an extension of ruppert s delaunay refinement algorithm to two dimensional domains with curved boundaries and prove that the same quality bounds apply with curved boundaries as with straight boundaries we provide implementation details for two dimensional boundary patches such as lines circular arcs cubic parametric curves and interpolated splines we present guaranteed quality triangular meshes generated with curved boundaries and propose solutions to some problems associated with the use of curved boundaries copyright 2002 john wiley sons ltd

a pro l version of the congruence subgroup problem for mapping class groups of genus one abstract let l be a prime number in the present paper we discuss a pro l version of the congruence subgroup problem for mapping class groups of genus one our main result is that the pro 2 version has an affirmative answer but the pro l version for l 11 has a negative answer

perturbation theory for the random dimer model the authors study a one dimensional tight binding model with a random potential taking two values or nu with the restriction that on pairs of two neighbouring sites the potentials take the same value this random dimer model proposed by dunlap phillips and wu 1990 has a vanishing lyapunov exponent for the energy e or nu they compute the lyapunov exponent and the density of states perturbatively in the vicinity of this energy using the invariant measure formalism

double shuffle relation for associators it is proved that drinfel 0 d s pentagon equation implies the generalized double shue relation as a corollary an embedding from the grothen

generalized log sine integrals and the mordell tornheim zeta values we introduce certain integrals of a product of the bernoulli polynomials and logarithms of milnor s multiple sine functions it is shown that all the integrals are expressed by the mordell tornheim zeta values at positive integers and that the converse is also true moreover we apply the theory of the integral to obtain various new results for the mordell tornheim zeta values

differentials on graph complexes abstract we study the cohomology of complexes of ordinary non decorated graphs introduced by m kontsevich we construct spectral sequences converging to zero whose first page contains the graph cohomology in particular these spectral sequences may be used to show the existence of an infinite series of previously unknown and provably non trivial cohomology classes and put constraints on the structure of the graph cohomology as a whole

the depth structure of motivic multiple zeta values in this paper we construct some maps related to the motivic galois action on depth graded motivic multiple zeta values from these maps we give some short exact sequences about depth graded motivic multiple zeta values in depth two and three in higher depth we conjecture that there are exact sequences of the same type we will show from three conjectures about depth graded motivic lie algebra we can nearly deduce the exact sequences conjectures in higher depth at last we give a new proof of the result that the modulo zeta mathfrak m 2 version motivic double zeta values are generated by the totally odd part we reduce the well known conjecture that the modulo zeta mathfrak m 2 version motivic triple zeta values are generated by the totally odd part to an isomorphism conjecture in linear algebra

algebraic differential formulas for the shuffle stuffle and duality relations of iterated integrals abstract in this paper we prove certain algebraic identities which correspond to differentiation of the shuffle relation the stuffle relation and the relations which arise from mobius transformations of iterated integrals these formulas provide fundamental and useful tools in the study of iterated integrals on a punctured projective line

evaluation of the multiple zeta values zeta 2 dots 2 3 2 dots 2 a formula is given for the special multiple zeta values occurring in the title as rational linear combinations of products m p 2n with m odd the existence of such a formula had been proved using motivic arguments by francis brown but the explicit formula more precisely certain 2 adic properties of its coefficients were needed for his proof in cite1 of the conjecture that all periods of mixed tate motives over z are q 2pi 1 linear combinations of multiple zeta values the formula is proved indirectly by computing the generating functions of both sides in closed form one as the product of a sine function and a 3 f 2 hypergeometric function and one as a sum of 14 products of sine functions and digamma functions and then showing that both are entire functions of exponential growth and that they agree at sufficiently many points to force their equality we also show that the space spanned by the multiple zeta values in question coincides with the space of double zeta values of odd weight and find a relation between this space and the space of cusp forms on the full modular group

new properties of multiple harmonic sums modulo p and p analogues of leshchiner s series in this paper we present some new identities of hypergeometric type for multiple harmonic sums whose indices are the sequences 1 a c 1 b 2 a c 2 b and prove a number of congruences for these sums modulo a prime p the congruences obtained allow us to find nice p analogues of leshchiner s series for zeta values and to refine a result due to m hoffman and j zhao about the set of generators of the multiple harmonic sums of weight 7 and 9 modulo p moreover we are also able to provide a new proof of zagier s formula for zeta 2 a 3 2 b based on a finite identity for partial sums of the zeta star series

shuffle relations for regularised integrals of symbols we prove shuffle relations which relate a product of regularised integrals of classical symbols int reg sigma i d xi i i 1 ldots k to regularised nested iterated integrals prod i 1 k int reg sigma i d xi i sum tau in sigma k int reg d xi 1 int vert xi 2 vert leq vert xi 1 vert d xi 2 cdots int vert xi l vert leq vert xi k 1 vert d xi k otimes i 1 k sigma tau i where k is the group of permutations over k elements we show that these shuffle relations hold if all the symbols i have vanishing residue this is true of non integer order symbols on which the regularised integrals have all the expected properties such as stokes property mmp in general the shuffle relations hold up to finite parts of corrective terms arising from a renormalisation on tensor products of classical symbols a procedure adapted from renormalisation methods to compute feynman diagrams familiar to physicists we relate the shuffle relations for regularised integrals of symbols with shuffle relations for multiple zeta functions adapting the above constructions to the case of a symbol on the unit circle

double shuffle relations for arborified zeta values abstract arborified zeta values are defined as iterated series and integrals using the universal properties of rooted trees this approach allows to study their convergence domain and to relate them to multiple zeta values generalisations to rooted trees of the stuffle and shuffle products are defined and studied it is further shown that arborified zeta values are algebra morphisms for these new products on trees

kontsevich s graph complex grt and the deformation complex of the sheaf of polyvector fields we generalize kontsevich s construction of l1 derivations of polyvector elds from the ane space to an arbitrary smooth algebraic variety more precisely we construct a map in the homotopy category from kontsevich s graph complex to the deformation complex of the sheaf of polyvector elds on a smooth algebraic variety we show that the action of deligne drinfeld

quantum quasi shuffle algebras ii we establish some properties of quantum quasi shuffle algebras they include the necessary and sufficient condition for the construction of the quantum quasi shuffle product the universal property and the commutativity condition as an application we use the quantum quasi shuffle product to construct a linear basis of t v for a special kind of yang baxter algebras v m

the genus and a regularization of an s1 equivariant euler class we show that a new multiplicative genus in the sense of hirzebruch can be obtained by generalizing a calculation due to atiyah and witten we introduce this as the genus compute its value for some examples and highlight some of its interesting properties we also indicate a connection with the study of multiple zeta values which gives an algebraic interpretation for our proposed regularization procedure

m kontsevich s graph complex and the grothendieck teichmuller lie algebra we show that the zeroth cohomology of m kontsevich s graph complex is isomorphic to the grothendieck teichmuller lie algebra mathfrak grt 1 the map is explicitly described this result has applications to deformation quantization and duflo theory we also compute the homotopy derivations of the gerstenhaber operad they are parameterized by mathfrak grt 1 up to one class or two depending on the definitions more generally the homotopy derivations of the non unital e n operads may be expressed through the cohomology of a suitable graph complex our methods also give a second proof of a result of h furusho stating that the pentagon equation for mathfrak grt 1 elements implies the hexagon equation

finite correlation dimension for stochastic systems with power law spectra abstract we discuss a counter example to the traditional view that stochastic processes lead to a non convergence of the correlation dimension in computed or measured time series specifically we show that a simple class of colored random noises characterized by a power law power spectrum have a finite and predictable value for the correlation dimension these results have implications on the experimental study of deterministic chaos as they indicate that the soie observation of a finite fractal dimension from the analysis of a time series is not sufficient to infer the presence of a strange attractor in the system dynamics we demonstrate that the types of random noises considered herein may be given an interpretation in terms of their fractal properties the consequent exploitation of the non gaussian behavior of these random noises leads us to the introduction of a new time series analysis method which we call multivariate scaling analysis we apply this approach to characterize several global properties of random noise

relations of multiple zeta values and their algebraic expression abstract we establish a new class of relations which we call the cyclic sum identities among the multiple zeta values k1 kl n1 nl 11 n1k1 nkkl these identities have an elementary proof and imply the sum theorem for multiple zeta values they also have a succinct statement in terms of cyclic derivations as introduced by rota sagan and stein in addition we discuss the expression of other relations of multiple zeta values via the shuffle and harmonic products on the underlying vector space h of the noncommutative polynomial ring q x y and also using an action of the hopf algebra of quasi symmetric functions on q x y

on the statistics of superlocalized states in self affine disordered potentials we investigate the statistics of eigenstates in a weak self affine disordered potential in one dimension whose gaussian fluctuations grow with distance with a positive hurst exponent h typical eigenstates are superlocalized on samples much larger than a well defined crossover length which diverges in the weak disorder regime we present a parallel analytical investigation of the statistics of these superlocalized states in the discrete and the continuum formalisms for the discrete tight binding model the effective localization length decays logarithmically with the sample size and the logarithm of the transmission is marginally self averaging for the continuum schrodinger equation the superlocalization phenomenon has more drastic effects the effective localization length decays as a power of the sample length and the logarithm of the transmission is fully non self averaging

the combinatorial hopf algebra of motivic dissection polylogarithms abstract we introduce a family of periods of mixed tate motives called dissection polylogarithms that are indexed by combinatorial objects called dissection diagrams the motivic coproduct on the former is encoded by a combinatorial hopf algebra structure on the latter this generalizes goncharov s formula for the motivic coproduct on generic iterated integrals our main tool is the study of the relative cohomology group corresponding to a bi arrangement of hyperplanes

multiple series connected to hoffman s conjecture on multiple zeta values abstract recent results of zlobin and cresson fischler rivoal allow one to decompose any suitable p uple series of hypergeometric type into a linear combination over the rationals of multiple zeta values of depth at most p in some cases only the multiple zeta values with 2 s and 3 s are involved as in hoffman s conjecture in this text we study the depth p part of this linear combination namely the contribution of the multiple zeta values of depth exactly p we prove that it satisfies some symmetry property as soon as the p uple series does and make some conjectures on the depth p 1 part of the linear combination when p 3 our result generalizes the property that very well poised univariate hypergeometric series involve only zeta values of a given parity which is crucial in the proof by rivoal and ball rivoal that 2 n 1 is irrational for infinitely many n 1 the main feature of the proof is an algebraic approach based on representations of z 2 z p s p

double zeta values double eisenstein series and modular forms of level 2 we study the double shuffle relations satisfied by the double zeta values of level 2 and introduce the double eisenstein series of level 2 which satisfy the double shuffle relations we connect the double eisenstein series to modular forms of level 2

duality between quasi symmetrical functions and the solomon descent algebra abstract the ring qsym of quasi symmetric functions is naturally the dual of the solomon descent algebra the product and the two coproducts of the first extending those of the symmetric functions correspond to a coproduct and two products of the second which are defined by restriction from the symmetric group algebra a consequence is that qsym is a free commutative algebra

the frobenius properad is koszul we show koszulness of the prop governing involutive lie bialgebras and also of the props governing non unital and unital counital frobenius algebras solving a long standing problem this gives us minimal models for their deformation complexes and for deformation complexes of their algebras which are discussed in detail using an operad of graph complexes we prove with the help of an earlier result of one of the authors that there is a highly non trivial action of the grothendieck teichm uller group grt 1 on completed versions of the minimal models of the properads governing lie bialgebras and involutive lie bialgebras by automorphisms as a corollary one obtains a large class of universal deformations of any involutive lie bialgebra and any frobenius algebra parameterized by elements of the grothendieck teichm uller lie algebra we also prove that for any given homotopy involutive lie bialgebra structure in a vector space there is an associated homotopy batalin vilkovisky algebra structure on the associated chevalley eilenberg complex

motivic structures on higher homotopy groups of hyperplane arrangements in this note we show the existence of motivic structures on certain objects arising from the higher rational homotopy groups of non nilpotent spaces examples of such spaces include several families of hyperplane arrangements in particular we construct an object in nori s category of motives whose realization is a certain completion of pi n mathbb p n setminus l 1 ldots l n 2 where the l i are hyperplanes in general position similar results are shown to hold in vovoedsky s setting of mixed motives

3d phase field simulations of interfacial dynamics in newtonian and viscoelastic fluids this work presents a three dimensional finite element algorithm based on the phase field model for computing interfacial flows of newtonian and complex fluids a 3d adaptive meshing scheme produces fine grid covering the interface and coarse mesh in the bulk it is key to accurate resolution of the interface at manageable computational costs the coupled navier stokes and cahn hilliard equations plus the constitutive equation for non newtonian fluids are solved using second order implicit time stepping within each time step newton iteration is used to handle the nonlinearity and the linear algebraic system is solved by preconditioned krylov methods the phase field model with a physically diffuse interface affords the method several advantages in computing interfacial dynamics one is the ease in simulating topological changes such as interfacial rupture and coalescence another is the capability of computing contact line motion without invoking ad hoc slip conditions as validation of the 3d numerical scheme we have computed drop deformation in an elongational flow relaxation of a deformed drop to the spherical shape and drop spreading on a partially wetting substrate the results are compared with numerical and experimental results in the literature as well as our own axisymmetric computations where appropriate excellent agreement is achieved provided that the 3d interface is adequately resolved by using a sufficiently thin diffuse interface and refined grid since our model involves several coupled partial differential equations and we use a fully implicit scheme the matrix inversion requires a large memory this puts a limit on the scale of problems that can be simulated in 3d especially for viscoelastic fluids

duality and q multiple zeta values abstract following bachmann s recent work on bi brackets and multiple eisenstein series zudilin introduced the notion of multiple q zeta brackets which provides a q analog of multiple zeta values possessing both shuffle as well as quasi shuffle relations the corresponding products are related in terms of duality in this work we study zudilin s duality construction in the context of classical multiple zeta values as well as various q analogs of multiple zeta values regarding the former we identify the derivation relation of order two with a hoffman ohno type relation then we describe relations between the ohno okuda zudilin q multiple zeta values and the schlesinger zudilin q multiple zeta values

alternating multizeta values in positive characteristic we introduce alternating multizeta values in positive characteristic which are generalizations of thakur multizeta values we establish their fundamental properties including non vanishing sum shuffle relations period interpretation and linear independence which is a direct sum result for these values

delocalization phenomena in one dimensional models with long range correlated disorder a perturbative approach we study the nature of electronic states in one dimensional continuous models with weak correlated disorder using a perturbative approach we compute the inverse localization length lyapunov exponent up to terms proportional to the fourth power of the potential this makes it possible to analyse the delocalization transition which takes place when the disorder exhibits specific long range correlations we find that the transition consists of a change of the lyapunov exponent which switches from a quadratic to a quartic depending on the strength of the disorder within the framework of the fourth order approximation we also discuss the different localization properties which distinguish gaussian from non gaussian random potentials

correlation induced metal insulator transition in the one dimensional anderson model abstract we study the nature of the electronic states in tight binding one dimensional models with long range correlated disorder in particular we study both diagonal and off diagonal chains the energies are considered to be in such a sequency to describe the trace of a fractional brownian motion with a specified spectral density s k 1 k using a renormalization group technique we show that for random on site energy sequences with anti persistent increments 2 the lyapunov coefficient inverse localization length vanishes within a finite range of energy values revealing the presence of an anderson like metal insulator transition in the case of off diagonal disorder a phase of delocalized states becomes stable for any 1

renormalization of multiple zeta values abstract multiple zeta values mzvs in the usual sense are the special values of multiple variable zeta functions at positive integers their extensive studies are important in both mathematics and physics with broad connections and applications in contrast very little is known about the special values of multiple zeta functions at non positive integers since the values are usually undefined we define and study multiple zeta functions at integer values by adapting methods of renormalization from quantum field theory and following the hopf algebra approach of connes and kreimer this definition of renormalized mzvs agrees with the convergent mzvs and extends the work of ihara kaneko zagier on renormalization of mzvs with positive arguments we further show that the important quasi shuffle stuffle relation for usual mzvs remains true for the renormalized mzvs

the algebra of multitangent functions abstract multizeta values are numbers appearing in many different contexts unfortunately their arithmetics remains mostly out of reach in this article we define a functional analogue of the algebra of multizeta values namely the algebra of multitangent functions which are 1 periodic functions defined by a process formally similar to multizeta values we introduce here the fundamental notions of reduction into monotangent functions projection onto multitangent functions and that of trifactorization giving a way of writing a multitangent function in terms of hurwitz multizeta functions this explains why the multitangent algebra is a functional analogue of the algebra of multizeta values we then discuss the most important algebraic and analytic properties of these functions and their consequences on multizeta values as well as their regularization in the divergent case each property of multitangents has a pendant on the side of multizeta values this allows us to propose new conjectures which have been checked up to the weight 18

motivic multiple zeta values and superstring amplitudes the structure of tree level open and closed superstring amplitudes is analyzed for the open superstring amplitude we find a striking and elegant form which allows one to disentangle its expansion into several contributions accounting for different classes of multiple zeta values this form is bolstered by the decomposition of motivic multiple zeta values i e the latter encapsulate the expansion of the superstring amplitude moreover a morphism induced by the coproduct maps the expansion onto a non commutative hopf algebra this map represents a generalization of the symbol of a transcendental function in terms of elements of this hopf algebra the expansion assumes a very simple and symmetric form which carries all the relevant information equipped with these results we can also cast the closed superstring amplitude into a very elegant form

mixed tate motives over z we prove that the category of mixed tate motives over z is spanned by the motivic fundamental group of p 1 minus three points we prove a conjecture by m hoffman which states that every multiple zeta value is a q linear combination of n 1 n r where n i 2 3