on zaremba s conjecture zaremba s 1971 conjecture predicts that every integer appears as the denominator of a nite continued fraction whose partial quotients are bounded by an absolute constant we conrm this conjecture for a set of density one

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

on the langlands functoriality for automorphic forms this is the extended notes of my lcctures on the langlands functoriality of automorphic forms which are in particular on the topics closely related to my recent work

sums of kloosterman sums in arithmetic progressions and the error term in the dispersion method we prove a bound for quintilinear sums of kloosterman sums with congruence conditions on the smooth summation variables this generalizes classical work of deshouillers and iwaniec and is key to obtaining power saving error terms in applications notably the dispersion method as a consequence assuming the riemann hypothesis for dirichlet l functions we prove a power saving error term in the titchmarsh divisor problem of estimating sum p leq x tau p 1 unconditionally we isolate the possible contribution of siegel zeroes showing it is always negative extending work of fouvry and tenenbaum we obtain power saving in the asymptotic formula for sum n leq x tau k n tau n 1 reproving a result announced by bykovski u i and vinogradov by a different method the gain in the exponent is shown to be independent of k if a generalized lindel of hypothesis is assumed

on largeness and multiplicity of the first eigenvalue of finite area hyperbolic surfaces we apply topological methods to study the smallest non zero number lambda 1 in the spectrum of the laplacian on finite area hyperbolic surfaces for closed hyperbolic surfaces of genus two we show that the set s in mathcal m 2 lambda 1 s frac 1 4 is unbounded and disconnects the moduli space mathcal m 2 using this for genus g ge 3 we show the existence of eigenbranches that start as lambda 1 and eventually becomes frac 1 4

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

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 implicit integration algorithm with a projection method for viscoplastic constitutive equations robinson s viscoplastic model a representative of the so called overstress models is integrated by use of the generalized midpoint rule the solution of the non linear system of algebraic equations arising from time discretization of the constitutive equations is determined using a projection method in combination with newton s method consistent tangent moduli are calculated and the quadratic convergence of the global newton equilibrium iteration is shown the time increment size is controlled by the convergence behaviour of the equilibrium iteration and the accuracy of the numerical integration various numerical examples are considered to demonstrate the efficiency of the methods

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

consistent tangent operators for rate independent elastoplasticity abstract it is shown that for problems involving rate constitutive equations such as rate independent elastoplasticity the notion of consistency between the tangent stiffness operator and the integration algorithm employed in the solution of the incremental problem plays a crucial role in preserving the quadratic rate of asymptotic convergence of iterative solution schemes based upon newton s method within the framework of closest point projection algorithms a methodology is presented whereby tangent operators consistent with this class of algorithms may be systematically developed to wit associative j 2 flow rules with general nonlinear kinematic and isotropic hardening rules as well as a class of non associative flow rules are considered the resulting iterative solution scheme preserves the asymptotic quadratic convergence characteristic of newton s method whereas use of the socalled elastoplastic tangent in conjunction with a radial return integration algorithm a procedure often employed results in newton type of algorithms with suboptimal rate of convergence application is made to a set of numerical examples which include saturation hardening laws of exponential type

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

twisted moments of l functions and spectral reciprocity we establish a reciprocity formula that expresses the fourth moment of automorphic l functions of level q twisted by the lth hecke eigenvalue as the fourth moment of automorphic l functions of level l twisted by the qth hecke eigenvalue direct corollaries include subconvexity bounds for l functions in the level aspect and a short proof of an upper bound for the fifth moment of automorphic l functions

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

numerical finite element formulation of the schapery non linear viscoelastic material model this study presents a numerical integration method for the non linear viscoelastic behaviour of isotropic materials and structures the schapery s three dimensional 3d non linear viscoelastic material model is integrated within a displacement based finite element fe environment the deviatoric and volumetric responses are decoupled and the strain vector is decomposed into instantaneous and hereditary parts the hereditary strains are updated at the end of each time increment using a recursive formulation the constitutive equations are expressed in an incremental form for each time step assuming a constant incremental strain rate a new iterative procedure with predictor corrector type steps is combined with the recursive integration method a general polynomial form for the parameters of the non linear schapery model is proposed the consistent algorithmic tangent stiffness matrix is realized and used to enhance convergence and help achieve a correct convergent state verifications of the proposed numerical formulation are performed and compared with a previous work using experimental data for a glassy amorphous polymer pmma copyright 2003 john wiley sons ltd

the second moment of gl 4 gl 2 l functions at special points abstract in this paper we obtain upper bounds for the second moment of l u j 1 2 i t j where is a hecke maass form for s l 4 z and u j is taken from an orthonormal basis of hecke maass forms on s l 2 z with eigenvalue 1 4 t j 2 the bounds are consistent with the lindelof hypothesis previously these types of upper bounds are available for only g l n g l 2 where n 3

new bounds in reduction theory of indefinite ternary integral quadratic forms abstract using dynamics on homogeneous spaces we obtain some new and improved estimates for reduction of indefinite ternary integral quadratic forms

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

a uniform spectral gap for congruence covers of a hyperbolic manifold let g be rm so n 1 or rm su n 1 and let gamma subset g denote an arithmetic lattice the hyperbolic manifold gamma backslash cal h comes with a natural family of covers coming from the congruence subgroups of gamma in many applications it is useful to have a bound for the spectral gap that is uniform for this family when gamma is itself a congruence lattice there are very good bounds coming from known results towards the ramanujan conjectures in this paper we establish an effective bound that is uniform for congruence subgroups of a non congruence lattice

the role of the ramanujan conjecture in analytic number theory we discuss progress towards the ramanujan conjecture for the group gln and its relation to various other topics in analytic number theory

a three dimensional finite element formulation for thermoviscoelastic orthotropic media summary this paper is concerned with the development of a numerical algorithm for the solution of the uncoupled quasistatic initial boundary value problem involving orthotropic linear viscoelastic media undergoing thermal and or mechanical deformation the constitutive equations expressed in integral form involving the relaxation moduli are transformed into an incremental algebraic form prior to development of the nite element formulation this incrementalization is accomplished in closed form and results in a recursive relationship which leads to the need of solving a simple set of linear algebraic equations only for the extraction of the nite element solution use is made of a dirichlet prony series representation of the relaxation moduli in order to derive the recursive relationship and thereby eliminate the storage problem that arises when dealing with materials possessing memory three illustrative example problems are included to demonstrate the method 1997 by john wiley sons ltd

a time integration method for the viscoelastic viscoplastic analyses of polymers and finite element implementation the present study introduces a time integration algorithm for solving a non linear viscoelastic viscoplastic ve vp constitutive equation of isotropic polymers the material parameters in the constitutive models are stress dependent the algorithm is derived based on an implicit time integration method computational inelasticity springer new york 1998 within a general displacement based finite element fe analysis and suitable for small deformation gradient problems schapery s integral model is used for the ve responses while the vp component follows the perzyna model having an overstress function a recursive iterative method int j numer meth engng 2004 59 25 45 is employed and modified to solve the ve vp constitutive equation an iterative procedure with predictor corrector steps is added to the recursive integration method a residual vector is defined for the incremental total strain and the magnitude of the incremental vp strain a consistent tangent stiffness matrix as previously discussed in ju j eng mech 1990 116 1764 1779 and simo and hughes computational inelasticity springer new york 1998 is also formulated to improve convergence and avoid divergence available experimental data on time dependent and inelastic responses of high density polyethylene are used to verify the current numerical algorithm the time integration scheme is examined in terms of its computational efficiency and accuracy numerical fe analyses of microstructural responses of polyethylene reinforced with elastic particle are also presented copyright 2009 john wiley sons ltd

level raising and symmetric power functoriality iii we apply automorphy lifting techniques to establish new cases of symmetric power functoriality for hilbert modular forms of regular algebraic weight the proof is based on a novel application of an automorphy lifting theorem for residually reducible galois representations

viscoplasticity for instabilities due to strain softening and strain rate softening three viscoplastic approaches are examined in this paper first the overstress viscoplastic models i e the perzyna model and the duvaut lions model are outlined next a consistency viscoplastic approach is presented in the consistency model a rate dependent yield surface is employed while the standard kuhn tucker conditions for loading and unloading remain valid for this reason the yield surface can expand and shrink not only by softening or hardening e ects but also by softening hardening rate e ects a full algorithmic treatment is presented for each of the three models including the derivation of a consistent tangential sti ness matrix based on a limited numerical experience it seems that the consistency model shows a faster global convergence than the overstress approaches for softening problems all three approaches have a regularising e ect in the sense that the initial value problem remains well posed the width of the shear band is determined by the material parameters and if present by the size of an imperfection a relation between the length scales of the three models is given furthermore it is shown that the consistency model can properly simulate the so called s type instabilities which are associated with the occurrence of travelling portevin le chatelier bands 1997 john wiley sons ltd

wave propagation and reflection transmission in a stratified viscoelastic solid abstract the paper investigates time harmonic wave propagation in continuously stratified solids and provides the results of a reflection transmission process generated by a layer sandwiched between homogeneous half spaces the layer is continuously stratified and allows for jump discontinuities at a finite number of planes the dissipative effects are accounted for through the classical boltzmann law of viscoelasticity by using displacement and traction as convenient vector variables the governing equations are considered in a vector volterra integral equation and the solution is determined by means of a matricant next the matricant is applied to determine the reflection and transmission coefficients of a layer with a generic piecewise continuous profile of the material properties the reflection transmission process produced by an obliquely incident wave is considered for horizontally polarized waves the low frequency approximation is derived for the reflection and transmission coefficients next the high frequency approximation is investigated by a wkb like procedure which involves a complex valued frequency dependent shear modulus the displacement solution is obtained for the forward and the backward propagating waves in the layer along with the reflection and transmission coefficients

prime and almost prime integral points on principal homogeneous spaces we develop the affine sieve in the context of orbits of congruence subgroups of semisimple groups acting linearly on affine space in particular we give effective bounds for the saturation numbers for points on such orbits at which the value of a given polynomial has few prime factors in many cases these bounds are of the same quality as what is known in the classical case of a polynomial in one variable where the orbit consists of the integers when the orbit is the set of integral matrices of a fixed determinant we obtain a sharp result for the saturation number and thus establish the zariski density of matrices all of whose entries are prime numbers among the key tools used are explicit approximations to the generalized ramanujan conjectures for such groups and sharp and uniform counting of points on such orbits when ordered by various norms

a finite element constitutive update scheme for anisotropic viscoelastic solids exhibiting non linearity of the schapery type this study presents a new scheme for performing integration point constitutive updates for anisotropic small strain non linear viscoelasticity within the context of implicit non linear finite element structural analysis while the basic scheme has been presented earlier by the authors for linear viscoelasticity the present work illustrates the generality of the underlying fundamentals by extending to schapery s non linear model the method features a judicious choice of state variables a stable backward euler integration step and a consistent tangent operator its greatest strength lies in ready incorporation into existing fem codes numerical examples involving homogeneous stress states such as uniaxial extension and simple shear and non uniform stress states such as a beam under tip load were carried out by incorporating the present scheme into a general purpose fem package excellent agreement with analytical results is observed copyright 1999 john wiley sons ltd

finiteness results for modular curves of genus at least 2 a curve x over inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 01i is modular if it is dominated by x 1 n for some n if in addition the image of its jacobian in j 1 n is contained in the new subvariety of j 1 n then x is called a new modular curve we prove that for each g 2 the set of new modular curves over inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 02i of genus g is finite and computable for the computability result we prove an algorithmic version of the de franchis severi theorem similar finiteness results are proved for new modular curves of bounded gonality for new modular curves whose jacobian is a quotient of j 0 n new with n divisible by a prescribed prime and for modular curves new or not with levels in a restricted set we study new modular hyperelliptic curves in detail in particular we find all new modular curves of genus 2 explicitly and construct what might be the complete list of all new modular hyperelliptic curves of all genera finally we prove that for each field k of characteristic zero and g 2 the set of genus g curves over k dominated by a fermat curve is finite and computable

counting lattice points for a locally compact second countable group g and a lattice subgroup we give an explicit quantitative solution of the lattice point counting problem in general domains in g provided that i g has finite upper local dimension and the domains satisfy a basic regularity condition ii the mean ergodic theorem for the action of g on g holds with a rate of convergence the error term we establish matches the best current result for balls in symmetric spaces of simple higher rank lie groups but holds in much greater generality a significant advantage of the ergodic theoretic approach we use is that the solution to the lattice point counting problem is uniform over families of lattice subgroups provided they admit a uniform spectral gap in particular the uniformity property holds for families of finite index subgroups satisfying a quantitative variant of property we discuss a number of applications including counting lattice points in general domains in semisimple s algebraic groups counting rational points on group varieties with respect to a height function and quantitative angular or conical equidistribution of lattice points in symmetric spaces and in affine symmetric varieties we note that the mean ergodic theorems which we establish are based on spectral methods including the spectral transfer principle and the kunze stein phenomenon we formulate and prove appropriate analogues of both of these results in the set up of adele groups and they constitute a necessary step in our proof of quantitative results in counting rational points

coupled viscoelastic viscoplastic modeling of homogeneous and isotropic polymers numerical algorithm and analytical solutions a coupled viscoelastic viscoplastic ve vp model is implemented and studied the total strain is the sum of ve and vp parts and the cauchy stress is given by a linear ve model as a boltzmann integral of the history of ve strains the proposed computational algorithm features fully implicit integration return mapping based on a two step ve predictor vp corrector strategy and a consistent tangent operator the algorithm is applied to j2 vp coupled with ve very compact expressions are obtained which are form identical to classical elasto viscoplasticity evp provided that the constant linear elastic shear and bulk moduli are replaced with incremental relaxation moduli which are appropriate functions of the time increment two different integration methods to obtain the incremental moduli are proposed and assessed closed form solutions for uniaxial tension and simple shear are developed based on an original solution method for integro differential equations the analytical results enable to illustrate the constitutive model and provide unambiguous benchmarks for numerical algorithms model predictions are compared with experimental data and reasonable correlation is obtained

bounding sup norms of cusp forms of large level let f be an l2 normalized weight zero hecke maas cusp form of square free level n character and laplacian eigenvalue 1 4 it is shown that f n 1 37 from which the hybrid bound f 1 4 n for some 0 is derived the first bound holds also for f yk 2f where f is a holomorphic cusp form of weight k with the implied constant now depending on k

eigenform product identities for hilbert modular forms we prove that amongst all real quadratic fields and all spaces of hilbert modular forms of full level and of weight 2 or greater the product of two hecke eigenforms is not a hecke eigenform except for finitely many real quadratic fields and finitely many weights we show that for mathbb q sqrt 5 there are exactly two such identities

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

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

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

weak subconvexity without a ramanujan hypothesis we describe a new method to obtain weak subconvexity bounds for l functions with mild hypotheses on the size of the dirichlet coefficients we verify these hypotheses for all automorphic l functions and with mild restrictions the rankin selberg l functions attached to two automorphic representations the proof relies on a new unconditional log free zero density estimate for rankin selberg l functions

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

generic transfer for general spin groups we prove langlands functoriality for the generic spectrum of general spin groups both odd and even contrary to other recent instances of functoriality our resulting automorphic representations on the general linear group are not self dual together with cases of classical groups this completes the list of cases of split reductive groups whose l groups have classical derived groups the important transfer from gsp4 to gl4 follows from our result as a special case

standard zero free regions for rankin selberg l functions via sieve theory we give a simple proof of a standard zero free region in the t aspect for the rankin selberg l function l s pi times widetilde pi for any unitary cuspidal automorphic representation pi of mathrm gl n mathbb a f that is tempered at every nonarchimedean place outside a set of dirichlet density zero

a thermo viscoelastic viscoplastic viscodamage constitutive model for asphaltic materials a temperature dependent viscodamage model is proposed and coupled to the temperature dependent schapery s nonlinear viscoelasticity and the temperature dependent perzyna s viscoplasticity constitutive model presented in abu al rub et al 2009 and huang et al in press in order to model the nonlinear constitutive behavior of asphalt mixes the thermo viscodamage model is formulated to be a function of temperature total effective strain and the damage driving force which is expressed in terms of the stress invariants of the effective stress in the undamaged configuration this expression for the damage force allows for the distinction between the influence of compression and extension loading conditions on damage nucleation and growth a systematic procedure for obtaining the thermo viscodamage model parameters using creep test data at different stress levels and different temperatures is presented the recursive iterative and radial return algorithms are used for the numerical implementation of the nonlinear viscoelasticity and viscoplasticity models respectively whereas the viscodamage model is implemented using the effective undamaged configuration concept numerical algorithms are implemented in the well known finite element code abaqus via the user material subroutine umat the model is then calibrated and verified by comparing the model predictions with experimental data that include creep recovery creep and uniaxial constant strain rate tests over a range of temperatures stress levels and strain rates it is shown that the presented constitutive model is capable of predicting the nonlinear behavior of asphaltic mixes under different loading conditions

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

a note on maass forms of icosahedral type using ideas of ramakrishnan we consider the icosahedral analogue of the theorems of sarnak and brumley on hecke maass newforms with fourier coefficients in a quadratic order although we are unable to conclude the existence of an associated galois representation in this case we show that one can deduce some implications of such an association including weak automorphy of all symmetric powers and the value distribution of fourier coefficients predicted by the chebotarev density theorem

the spectral decomposition of theta 2 let theta be an elementary theta function such as the classical jacobi theta function we establish a spectral decomposition and surprisingly strong asymptotic formulas for langle theta 2 varphi rangle as varphi traverses a sequence of hecke translates of a nice enough fixed function the subtlety is that typically theta 2 notin l 2 applications to the subconvexity quantum variance and 4 norm problems we determine all pairs a f g a g h of generalized weighted quasi arithmetic means being square iterative roots of a f g a g h that is the equation a f g a g h circ a f g a g h a f g a g h is solved under three times differentiability of the functions f g h f g h as an application some special cases are presented are indicated

on the pair correlation density for hyperbolic angles we prove a conjecture of boca popa zaharescu on the density function for the pair correlation of hyperbolic angles in a growing orbit of a discrete lattice in psl2 r

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

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 selberg s small eigenvalue conjecture and residual eigenvalues we show that selberg s eigenvalue conjecture concern ing small eigenvalues of the automorphic laplacian for congruence groups is equivalent to a conjecture about the non existence of residual eigenvalues for a perturbed system we prove this using a combination of methods from asymptotic perturbation theory and number theory