distribution of periodic torus orbits and duke s theorem for cubic fields we study periodic torus orbits on spaces of lattices using the action of the group of adelic points of the underlying tori we define a natural equivalence relation on these orbits and show that the equivalence classes become uniformly distributed this is a cubic analogue of duke s theorem about the distribution of closed geodesics on the modular surface suitably interpreted the ideal classes of a cubic totally real field are equidistributed in the modular 5 fold sl3 z sl3 r so3 in particular this proves a stronger form of the folklore conjecture that the collection of maximal compact flats in sl3 z sl3 r so3 of volume infinity

boundedness of automorphic l functions in vertical strips the purpose of this paper is to prove the boundedness in vertical strips of finite width for all the l functions that appear in constant terms of eisenstein series under a certain natural assumption on local normalized intertwining operators as a corollary we prove the boundedness for a number of important l functions among them the symmetic cube and triple product l functions attached to cusp forms on gl 2 as well as several rankin selberg product l functions where the local assumption was alredy proved to be valid in each case under the same assumption the finiteness of poles on all of c for all of these l functions is also proved a necessary step in the proof of boundedness in vertical strips

periodic homogenization for hypoelliptic diffusions we study the long time behavior of an ornstein uhlenbeck process under the influence of a periodic drift we prove that under the standard diffusive rescaling the law of the particle position converges weakly to the law of a brownian motion whose covariance can be expressed in terms of the solution of a poisson equation we also derive upper bounds on the convergence rate in several metrics

upper and lower bounds at s 1 for certain dirichlet series with euler product estimates of the form l j s mathscr a ll epsilon j mathscr d a mathscr r epsilon mathscr a in the range s 1 ll 1 log mathscr r a for general l functions where mathscr r a is a parameter related to the functional equation of l s mathscr a can be quite easily obtained if the ramanujan hypothesis is assumed we prove the same estimates when the l functions have euler product of polynomial type and the ramanujan hypothesis is replaced by a much weaker assumption about the growth of certain elementary symmetrical functions as a consequence we obtain an upper bound of this type for every l s pi where pi is an automorphic cusp form on rm gl mathbf d mathbb a k we employ these results to obtain siegel type lower bounds for twists by dirichlet characters of the third symmetric power of a maass form

equidistribution in shrinking sets and l 4 norm bounds for automorphic forms we study two closely related problems stemming from the random wave conjecture for maas forms the first problem is bounding the l 4 norm of a maas form in the large eigenvalue limit we complete the work of spinu to show that the l 4 norm of an eisenstein series e z 1 2 it g restricted to compact sets is bounded by sqrt log t g the second problem is quantum unique ergodicity in shrinking sets we show that by averaging over the centre of hyperbolic balls in gamma backslash mathbb h quantum unique ergodicity holds for almost every shrinking ball whose radius is larger than the planck scale this result is conditional on the generalised lindelof hypothesis for hecke maas eigenforms but is unconditional for eisenstein series we also show that equidistribution for hecke maas eigenforms need not hold at or below the planck scale finally we prove similar equidistribution results in shrinking sets for heegner points and closed geodesics associated to ideal classes of quadratic fields

on moments of twisted l functions we study the average of the product of the central values of two l functions of modular forms f and g twisted by dirichlet characters to a large prime modulus q as our principal tools we use spectral theory to develop bounds on averages of shifted convolution sums with differences ranging over multiples of q and we use the theory of deligne and katz to prove new bounds on bilinear forms in kloosterman sums with power savings when both variables are near the square root of q when at least one of the forms f and g is non cuspidal we obtain an asymptotic formula for the mixed second moment of twisted l functions with a power saving error term in particular when both are non cuspidal this gives a significant improvement on m young s asymptotic evaluation of the fourth moment of dirichlet l functions in the general case the asymptotic formula with a power saving is proved under a conjectural estimate for certain bilinear forms in kloosterman sums

an algebraic model for performance evaluation of timed event multigraphs this note demonstrated that a certain class of petri nets called timed event multigraphs can be represented as a set of linear equations by using a novel dioid with this new algebra some properties are presented in the text an example is discussed in the end and an interesting result is computed

modelling routing phenomenon with bounds estimation in dioids abstract in job shop systems each product is routed according to its own production cycle however routings or conflicts cannot be modelled in scalar dioid algebraic structures such as z min or z max also denoted z min and z max the main reason is that choices cannot be represented in such modellings in this article the input output behaviour of a whole system with several sub systems in conflict is bounded by those of two linear systems in dioid z min by doing so we model behaviours as intervals an interval contains all the possible system behaviours in terms of number of pallets coming and going delays and production rates when the routing policy therein is periodic as a consequence even though the input output behaviour of such a system is not linear in a scalar dioid we can nevertheless use an imprecise modelling over a dioid of intervals this allows for using dioid theory contributions as for control problem synthesis issues

cuspidality of symmetric powers with applications the purpose of this paper is to prove that the symmetric fourth power of a cusp form on rm gl 2 whose existence was proved earlier by the first author is cuspidal unless the corresponding automorphic representation is of dihedral tetrahedral or octahedral type as a consequence we prove a number of results toward the ramanujan petersson and sato tate conjectures in particular we establish the bound q sp 1 9 sb v for unramified hecke eigenvalues of cusp forms on rm gl 2 over an arbitrary number field this is the best bound available at present

twisted endoscopy and reducibility of induced representations for p adic groups 1 introduction this is the first in a series of papers in which we study the reducibility of representations induced from discrete series representations of the levi factors ofmaximal parabolic subgroups of p adic groups on the unitary axis the problem is equivalent to determining certain local langlands l functions which are of arithmetic significance by themselves one of the main aims of this paper is to interpret our results in the direction of the parametrization problem by means of the theory of twisted endoscopy for which our method seems to be very suitable when the representation is supercuspidal we also study the reducibility of the induced representations off the unitary axis let f be a p adic field of characteristic zero fix a positive integer n 1 and let g be either of the groups sp2n s02n or s02n l in all three cases there is a conjugacy class of maximal parabolic subgroups which has gl as its levi factor let p mn be the standard parabolic subgroup ofg in this conjugacy class then m gl let tr be a discrete series representation of m gln f and given s c let i s tr be the representation of g g f induced from tr r idet ls let i tr i 0 tr

on the local langlands conejcture mathrm gl n the cyclic case let f be a locally compact nonarchimedean field and p its residue characteristic let f be a separable algebraic closure of f wf the weil group of f over f e a character of fx of order n and e the corresponding character of wf then there exists a canonical map from the set of equivalence classes a of irreducible degree n representations of wf such that e a a to the set of equivalence classes 7r of admissible irreducible supercuspidal representations of gl n f verifying odet x 7t this map is shown to be bijective and to preserve e factors for pairs

une preuve simple des conjectures de langlands pour gl n sur un corps p adique let f be a finite extension of p for each integer n 1 we construct a bijection from the set f 0 n of isomorphism classes of irreducible degree n representations of the absolute weil group of f onto the set f 0 n of isomorphism classes of smooth irreducible supercuspidal representations of gl n f those bijections preserve epsilon factors for pairs and hence we obtain a proof of the langlands conjectures for gl n over f which is more direct than harris and taylor s our approach is global and analogous to the derivation of local class field theory from global class field theory we start with a result of kottwitz and clozel on the good reduction of some shimura varieties and we use a trick of harris who constructs non galois automorphic induction in certain cases

bounds for eigenforms on arithmetic hyperbolic 3 manifolds on a family of arithmetic hyperbolic 3 manifolds of square free level we prove an upper bound for the sup norm of hecke maas cusp forms with a power saving over the local geometric bound simultaneously in the laplacian eigenvalue and the volume by a novel combination of diophantine and geometric arguments in a noncommutative setting we obtain bounds as strong as the best corresponding results on arithmetic surfaces

bounds for rankin selberg integrals and quantum unique ergodicity for powerful levels reference epfl article 202508doi 10 1090 s0894 0347 2013 00779 1view record in web of science record created on 2014 10 23 modified on 2017 12 10

maass forms and the mock theta function f q let f q 1 sum n 1 infty alpha n q n be the well known third order mock theta of ramanujan in 1964 george andrews proved an asymptotic formula of the form begin aligned alpha n sum c le sqrt n psi n o epsilon left n epsilon right end aligned where psi n is an expression involving generalized kloosterman sums and the i bessel function andrews conjectured that the series converges to alpha n when extended to infinity and that it does not converge absolutely bringmann and ono proved the first of these conjectures here we obtain a power savings bound for the error in andrews formula and we also prove the second of these conjectures our methods depend on the spectral theory of maass forms of half integral weight and in particular on an average estimate for the fourier coefficients of such forms which gives a power savings in the spectral parameter as a further application of this result we derive a formula which expresses alpha n with small error as a sum of exponential terms over imaginary quadratic points this is similar in spirit to a recent result of masri we also obtain a bound for the size of the error term incurred by truncating rademacher s analytic formula for the ordinary partition function which improves a result of the first author and andersen when 24n 23 is squarefree

equidistribution of cusp forms in the level aspect let f traverse a sequence of classical holomorphic newforms of fixed weight and increasing square free level q infinity we prove that the pushforward of the mass off to the modular curve of level 1 equidistributes with respect to the poincare measure

on the ramanujan conjecture and finiteness of poles for certain l functions in this paper we prove a number of general results about automorphic l functions which appear in the constant terms of eisenstein series for an arbitrary quasi split connected reductive algebraic group over a number field these l functions were first introduced by langlands for chevalley groups 20 and through them he was led to make some of his deep conjectures 21 one significance of these l functions is that all the automorphic l functions studied so far are among them there are three general results first we obtain a uniform line of absolute convergence for all of these l functions theorem 5 1 a uniform estimate for the hecke eigenvalues of generic cusp forms on many absolutely simple quasi split connected reductive algebraic groups over number fields corollary 5 4 and an improvement on the best available estimate for the fourier coefficients of maass wave forms corollary 5 5 also follow next we establish a meromorphic continuation and functional equation for each of these l functions theorem 6 1 finally in theorem 6 2 we prove finiteness of poles on the whole complex plane for an important class of these l functions corollaries 6 6 through 6 10 more precisely let g be a quasi split connected reductive algebraic group over a number field f set g g a f where a f is the ring of adeles of f fix a borel subgroup b of g over f and let u be its unipotent radical let p be a maximal f parabolic subgroup of g with p d b in the context of the problems studied here nothing new will be obtained if one drops the maximality condition on p write p mn a levi decomposition n c u and let b u p m and n be the corresponding groups of adelic points for every place v of f let gv g fj similarly we have bv us pv me and nv let x xv be a generic character of u f u cf section 3 then each xv is generic let r ov 7tv be a cusp form on m we shall say 7t is

a proof of langland s conjecture on plancherel measures complementary series of p adic groups analysis of p adic reductive groups our first result theorem 7 9 proves a conjecture of langlands on normalization of intertwining operators by means of local langlands root numbers and l functions at least when the group is quasi split and the inducing representation is generic assuming two natural conjectures in harmonic analysis of p adic groups we also prove the validity of the conjecture in general theorem 9 5 as our second result we obtain all the complementary series and special representations of quasi split p adic groups coming from rank one parabolic subgroups and generic supercuspidal represen

quantum unique ergodicity for half integral weight automorphic forms we investigate the analogue of the quantum unique ergodicity que conjecture for half integral weight automorphic forms assuming the generalized riemann hypothesis grh we establish que for both half integral weight holomorphic hecke cusp forms for 0 4 lying in kohnen s plus subspace and for half integral weight hecke maa cusp forms for 0 4 lying in kohnen s plus subspace by combining the former result along with an argument of rudnick it follows that under grh the zeros of these holomorphic hecke cusp equidistribute with respect to hyperbolic measure on 0 4 h as the weight tends to infinity

rankin selberg l functions in the level aspect keywords moments rankin selberg convolution level aspect convexity breaking reference tan article 2002 003doi 10 1215 s0012 7094 02 11416 1 record created on 2008 11 14 modified on 2017 05 12

on the asymptotic behavior of an ornstein uhlenbeck process with random forcing we study the asymptotic behavior of an inertial tracer particle in a random force field we show that there exists a probability measure under which the process describing the velocity and environment seen from the vantage point of the moving particle is stationary and ergodic this measure is equivalent to the underlying probability for the eulerian flow as a consequence of the above we obtain the law of large numbers for the trajectory of the tracer moreover we prove also some decorrelation properties of the velocity of the particle which lead to the existence of a non degenerate asymptotic covariance tensor

modeling and control of weight balanced timed event graphs in dioids the class of timed event graphs tegs has widely been studied thanks to an approach known as the theory of max plus linear systems in particular the modeling of tegs via formal power series in a dioid called minax has led to input output representations on which some model matching control problems have been solved our work attempts to extend the class of systems for which a similar control synthesis is possible to this end a subclass of timed petri nets that we call weight balanced timed event graphs wbtegs will be first defined they can model synchronization and delays wbtegs contain tegs and can also describe dynamic phenomena such as batching and event duplications unbatching their behavior is described by rational compositions sum product and kleene star of four elementary operators n t m and b on a dioid of formal power series denoted e the main feature is that the transfer series of wbtegs have a property of ultimate periodicity such as rational series in minax finally the existing results on control synthesis for max plus linear systems find a natural application in this framework

lower estimates of transition densities and bounds on exponential ergodicity for stochastic pde s a formula for the transition density of a markov process defined by an infinite dimensional stochastic equation is given in terms of the ornstein uhlenbeck bridge and a useful lower estimate on the density is provided as a consequence uniform exponential ergodicity and v ergodicity are proved for a large class of equations we also provide computable bounds on the convergence rates and the spectral gap for the markov semigroups defined by the equations the bounds turn out to be uniform with respect to a large family of nonlinear drift coefficients examples of finite dimensional stochastic equations and semilinear parabolic equations are given

subconvex equidistribution of cusp forms reduction to eisenstein observables let traverse a sequence of cuspidal automorphic representations of gl2 with large prime level unramified central character and bounded infinity type for g gl1 pgl2 let h g denote the assertion that subconvexity holds for g twists of the adjoint l function of with polynomial dependence upon the conductor of the twist we show that h gl1 implies h pgl2 in geometric terms h pgl2 corresponds roughly to an instance of arithmetic quantum unique ergodicity with a power savings in the error term h gl1 to the special case in which the relevant sequence of measures is tested against an eisenstein series

on symmetric power l invariants of iwahori level hilbert modular forms we compute the arithmetic cal l invariants of greenberg benois of twists of symmetric powers of p adic galois representations attached to iwahori level hilbert modular forms under some technical conditions our method uses the automorphy of symmetric powers and the study of analytic galois representations on p adic families of automorphic forms over symplectic and unitary groups combining these families with some explicit plethysm in the representation theory of rm gl 2 we construct global galois cohomology classes with coefficients in the symmetric powers and provide formulae for the cal l invariants in terms of logarithmic derivatives of hecke eigenvalues

local coefficients as artin factors for real groups introduction the purpose of this paper is to prove the equality of certain local coefficients of arithmetic significance which were attached to representations of quasi split real reductive algebraic groups in 27 with their corresponding artin factors attached by local class field theory 21 as a consequence we establish an identity satisfied by certain normalized intertwining operators it seems to be useful in applications of the trace formula 1 29 more precisely let g be the group of real points of a quasi split reductive algebraic group over r let a be the set of simple roots defined by a fixed minimal parabolic subgroup po m0a0u of g fix 6 c a and let p p9 be the corresponding standard parabolic subgroup of g and write p man for its langlands decomposition fix a nondegenerate character x f u i a h o be an irreducible admissible x gic banach in particular x generic unitary representation of m cf section 1 given v g a the complex dual of the lie algebra of a let i v o 0 be the continuously quasi unitarily if o is unitary induced representation indp ga e v 9 and let v v o 0 be its space section 0 then f a vfoo o now let w be the weyl group of ao in g choose w g w such that w 0 c a let n be the unipotent group opposite to n define n u c wn w where w is a representative of w in g for g f a 00 define

trilinear forms and the central values of triple product l functions we give an explicit formula for certain global trilinear forms that appear in jacquet s conjecture in terms of local trilinear forms and the central values of triple product l functions

timed event graphs with multipliers and homogeneous min plus systems the authors study fluid analogues of a subclass of petri nets called fluid timed event graphs with multipliers which are a timed extension of weighted t systems studied in the petri net literature these event graphs can be studied naturally with a new algebra analogous to the min plus algebra but defined on piecewise linear concave increasing functions endowed with the pointwise minimum as addition and the composition of functions as multiplication a subclass of dynamical systems in this algebra which have a property of homogeneity can be reduced to standard min plus linear systems after a change of counting units the authors give a necessary and sufficient condition under which a fluid timed event graph with multipliers can be reduced to a fluid timed event graph without multipliers in the fluid case this class corresponds to the so called expansible timed event graphs with multipliers of munier 1993 or to conservative weighted t systems the change of variable is called here a potential its restriction to the transition nodes of the event graph is a t semiflow

weak subconvexity for central values of l functions we describe a general method to obtain weak subconvexity bounds for many classes of l functions we give several examples of our bound and our work has applications to a conjecture of rudnick and sarnak for the mass equidistribution of hecke eigenforms

sieving for mass equidistribution we approach the holomorphic analogue to the quantum unique ergodicity conjecture through an application of the large sieve we deal with shifted convolution sums as in ho109 with various simplifications in our analysis due to the knowledge of the ramanujan petersson conjecture in this holomorphic case

ohrnstein uhlenbeck process in a random potential on considere le processus d ohmstein uhlenbeck sur r d r d dans le potentiel aleatoire q x on montre que le processus d echelle x e t ex t e2 obeit au theoreme de la limite centrale en probabilite par rapport a

invariant distributions and time averages for horocycle flows there are infinitely many obstructions to existence of smooth solutions of the cohomological equation uu f where u is the vector field generating the horocycle flow on the unit tangent bundle sm of a riemann m surface of finite area and f is a given function on sm we study the sobolev regularity of these obstructions construct smooth solutions of the cohomological equation and derive asymptotics for the ergodic averages of horocycle flows

modularity of the rankin selberg l series and multiplicity one for sl 2 let f g be primitive cusp forms holomorphic or otherwise on the upper half plane h of levels n m respectively with unitarily normalized l functions l s f equation and l s g equation when p does not divide n resp m the inverse roots p p resp p p are nonzero with sum ap resp bp for every p prime to nm set lp s f g 1 p pp s 1 p pp s 1 p pp s 1 p pp s 1 let l s f g denote the incomplete euler product of lp s f g over all p not dividing nm this is closely related to the convolution l series sum over n 1 a sub n b sub n n s whose miraculous properties were first studied by rankin and selberg

on the arithmetic of shalika models and the critical values of l functions for gl2n let pi be a cohomological cuspidal automorphic representation of rm gl 2n bbb a over a totally real number field f suppose that pi has a shalika model we define a rational structure on the shalika model of pi f comparing it with a rational structure on a realization of pi f in cuspidal cohomology in top degree we define certain periods omega epsilon pi f we describe the behavior of such top degree periods upon twisting pi by algebraic hecke characters chi of f then we prove an algebraicity result for all the critical values of the standard l functions l s pi otimes chi here we use the recent work of b sun on the non vanishing of a certain quantity attached to pi infty as applications we obtain algebraicity results in the following cases firstly for the symmetric cube l functions attached to holomorphic hilbert modular cusp forms we also discuss the situation for higher symmetric powers secondly for certain self dual of symplectic type rankin selberg l functions for rm gl 3 times rm gl 2 assuming langlands functoriality this generalizes to certain rankin selberg l functions of rm gl n times rm gl n 1 thirdly for the degree four l functions attached to siegel modular forms of genus 2 and full level moreover we compare our top degree periods with periods defined by other authors we also show that our main theorem is compatible with conjectures of deligne and gross

kernels for products of hilbert l functions we study kernel functions of l functions and products of l functions of hilbert cusp forms over real quadratic fields this extends the results on elliptic modular forms in diamantis and o sullivan math ann 346 4 897 929 2010 algebra number theory 7 8 1883 1917 2013

mass equidistribution for hecke eigenforms in this work we study the mass equidistribution for holomorphic hecke eigenforms and establish by employing incomplete poincare series and the petersson formula sharp equidistribution results when the average is performed over intervals much shorter than before a key feature is the analysis of the off diagonal terms that result from this shortening of intervals 2003 wiley periodicals inc

real zeros and size of rankin selberg l functions in the level aspect in this paper some asymptotic formulas are proved for the harmonic mollified second moment of a family of rankin selberg l functions one of the main new input is a substantial improvement of the admissible length of the mollifier which is done by solving a shifted convolution problem by a spectral method on average a first consequence is a new subconvexity bound for rankin selberg l functions in the level aspect moreover infinitely many rankin selberg l functions having at most eight non trivial real zeros are produced and some new non trivial estimates for the analytic rank of the family studied are obtained

triple product formula and the subconvexity bound of triple product l function in level aspect in this paper we derive a nice general formula for the local integrals of triple product formula whenever one of the representations has sufficiently higher level than the other two as an application we generalize venkatesh and woodbury s work on the subconvexity bound of triple product l function in level aspect allowing joint ramifications higher ramifications general unitary central characters and general special values of local epsilon factors

the behaviour of eigenstates of arithmetic hyperbolic manifolds in this paper we study some problems arising from the theory of quantum chaos in the context of arithmetic hyperbolic manifolds we show that there is no strong localization scarring onto totally geodesic submanifolds arithmetic examples are given which show that the random wave model for eigenstates does not apply universally in 3 degrees of freedom

mass equidistribution for hecke eigenforms we prove a conjecture of rudnick and sarnak on the mass equidistribution of hecke eigenforms this builds upon independent work of the authors