the irreducibility of some level 1 hecke polynomials let t p k x be the characteristic polynomial of the hecke operator tp acting on the space of level 1 cusp forms s k 1 we show that t p k x is irreducible and has full galois group over q for k 2000 and p 2000 p prime

local influence to detect influential data structures for generalized linear mixed models biometrics 2001 dec 57 4 1166 72 related articles books linkout local influence to detect influential data structures for generalized linear mixed models ouwens mj tan fe berger mp department of methodology and statistics maastricht university the netherlands mario ouwens stat unimaas nl this article discusses the generalization of the local influence measures for normally distributed responses to local influence measures for generalized linear models with random effects for these models it is shown that the subject oriented influence measure is a special case of the proposed observation oriented influence measure a two step diagnostic procedure is proposed the first step is to search for influential subjects a search for influential observations is proposed as the second step an illustration of a two treatment multiple period crossover trial demonstrates the practical importance of the detection of influential observations in addition to the detection of influential subjects

some classes of generating functions associated with a certain family of extended and generalized hypergeometric functions recently srivastava et al 2012 11 introduced and initiated the study of many interesting fundamental properties and characteristics of a certain pair of potentially useful families of the so called generalized incomplete hypergeometric functions ever since then there have appeared many closely related works dealing essentially with notable developments involving various classes of generalized hypergeometric functions and generalized hypergeometric polynomials which are defined by means of the corresponding incomplete and other novel extensions of the familiar pochhammer symbol here in this sequel to some of these earlier works we first derive two remarkably distinct classes of hypergeometric generating functions and then apply each of them in deducing a family of linear bilinear and bilateral or mixed multilateral generating functions we also consider various known or new special cases and consequences of the results presented in this paper

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

shintani lifts and fractional derivatives for harmonic weak maass forms abstract in this paper we construct shintani lifts from integral weight weakly holomorphic modular forms to half integral weight weakly holomorphic modular forms although defined by different methods these coincide with the classical shintani lifts when restricted to the space of cusp forms as a side effect this gives the coefficients of the classical shintani lifts as new cycle integrals this yields new formulas for the l values of hecke eigenforms when restricted to the space of weakly holomorphic modular forms orthogonal to cusp forms the shintani lifts introduce a definition of weakly holomorphic hecke eigenforms along the way auxiliary lifts are constructed from the space of harmonic weak maass forms which yield a fractional derivative from the space of half integral weight harmonic weak maass forms to half integral weight weakly holomorphic modular forms this fractional derivative complements the usual operator introduced by bruinier and funke

mean square values of hecke l series formed with r th order characters let l be a number field containing the r th roots of unity starting with the rankin selberg convolution of a metaplectic eisenstein series on the r fold cover of gl 2 with itself we construct a dirichlet series defined over l whose coefficients involve the r th order twists of a fixed hecke l function we then observe that a group of functional equations can be naturally associated with this construction combining this with the convexity theorem for holomorphic functions of several complex variables we show that this object as a function of two complex variables admits meromorphic continuation to 2 as an application we obtain asymptotic formulae for mean square values of the r th order twists of an arbitrary hecke l function defined over l

on a generalization of gross s formula we prove a relation between whittaker functionals of cusp forms on widetilde sl 2 and the toric periods of forms on the quaternion algebra as an application we prove a generalization of a formula of gross

harmonic maass forms of weight 1 the object of this paper is to initiate a study of the fourier coefficients of a weight one harmonic maass form and relate them to the complex galois representation associated to a weight one newform which is the form s image under a certain differential operator in this paper our focus will be on weight one dihedral newforms of prime level p 3 mod 4 in this case we give properties of the fourier coefficients that are similar to and sometimes reduce to cases of stark s conjectures on derivatives of l functions we also give a new modular interpretation of certain products of differences of singular moduli studied by gross and zagier finally we provide some numerical evidence that the fourier coefficients of a mock modular form whose shadow is exotic are similarly related to the associated complex galois representation

central critical values of modular l functions and coefficients of half integral weight modular forms modulo l if f z is a newform of weight 2 and d is a fundamental discriminant then let l f d s be the usual twisted l series we study the algebraic parts of the central critical values of these twisted l series modulo primes we show that if there are two d subject to some local conditions for which the algebraic part of l f d is not 0 mod l then there are infinitely many such d these results depend on precise nonvanishing results for the fourier coefficients of half integral weight modular forms modulo l which are of independent interest

non vanishing of quadratic twists of modular l functions k have been the subject of much study both because of their intrinsicinterest and because of the prominent role they have played inkolyvagin s work on the birch and swinnerton dyer conjecture see b f h i j ko ma m m m1 o s p p waldspurger proved a fundamental theorem the ore me 1 w1 relating these central critical values to the fourier coe cients of half integral weight cusp forms for notational convenience if d is afundamental discriminant of a quadratic number eld then de ne d

the saito kurokawa lifting and darmon points let e mathbb q be an elliptic curve of conductor np with p not mid n and let f be its associated newform of weight 2 denote by f infty the p adic hida family passing though f and by f infty its varlambda adic saito kurokawa lift the p adic family f infty of siegel modular forms admits a formal fourier expansion from which we can define a family of normalized fourier coefficients widetilde a t k t indexed by positive definite symmetric half integral matrices t of size 2 times 2 we relate explicitly certain global points on e coming from the theory of darmon points with the values of these fourier coefficients and of their p adic derivatives evaluated at weight k 2

cycle integrals of the j function and mock modular forms in this paper we construct certain mock modular forms of weight 1 2 whose fourier coecients are given in terms of cycle integrals of the modular j function their shadows are weakly holomorphic forms of weight 3 2 these new mock modular forms occur as holomorphic parts of weakly harmonic maass forms we also construct a generalized mock modular form of weight 1 2 having a real quadratic class number times a regulator as a fourier coecient as an application of these forms we study holomorphic modular integrals of weight 2 whose rational period functions have poles at certain real quadratic integers the fourier coecients of these modular integrals are given in terms of cycle integrals of modular functions such a modular integral can be interpreted in terms of a shimura type lift of a mock modular form of weight 1 2 and yields a real quadratic analogue of a borcherds product

on the lifting of elliptic cusp forms to siegel cusp forms of degree 2n i 1 cf 8 in this paper we will prove that their conjecture is true moreover we obtain a simple fourier coefficient formula for f z ibukiyama 23 also made a similar conjecture which was formulated in terms of the koecher maass series which we will not consider here let us describe our results throughout this paper we fix positive integers k and n such that k n mod 2 and put e 1 k 1 n for any positive rational number n we denote the absolute value of the discriminant of q vn q by dn the primitive dirichlet character corresponding to q v n q is denoted by xn let fn be the positive rational number such that n nf2nlet b e m2n q be a positive definite half integral symmetric matrix put db det 2b db d db fb f db and xb x db note that edb 0 1 mod 4 and that fb is an integer for each prime p let p qp cx be the unique additive character such that bp x exp 27ir ltx for x e z p 1 recall that the siegel series for b is defined by

on the birch and swinnerton dyer conjecture let f be a finite extension of the rational field q if e is an elliptic curve defined over f then the mordell weil group e f of points on e with coordinates in f is a finitely generated abelian group let l e f s be the hasseweil zeta function of e over f which at least in the case where e has complex multiplication is known to be an analytic function on the entire complex plane birch and swinnerton dyer have conjectured that l e f s has a zero at s l of order precisely equal to the rank of e f over z the strongest result known in support of this conjecture is the following theorem of coates and wiles 4

distribution of mass of holomorphic cusp forms we prove an upper bound for the l4 norm and for the l2 norm restricted to the vertical geodesic of a holomorphic hecke cusp form f of large weight k the method is based on watson s formula and estimating a mean value of certain l functions of degree 6 further applications to restriction problems of siegel modular forms and subconvexity bounds of degree 8 l functions are given

beyond the excised ensemble modelling elliptic curve l functions with random matrices the excised ensemble a random matrix model for the zeros of quadratic twist families of elliptic curve l functions was introduced by duenez et al 2012 j phys a math theor 45 115207 the excised model is motivated by a formula for central values of these l functions in a paper by kohnen and zagier 1981 invent math 64 175 98 this formula indicates that for a finite set of l functions from a family of quadratic twists the central values are all either zero or are greater than some positive cutoff the excised model imposes this same condition on the central values of characteristic polynomials of matrices from strangely the cutoff on the characteristic polynomials that results in a convincing model for the l function zeros is significantly smaller than that which we would obtain by naively transferring kohnen and zagier s cutoff to the ensemble in this current paper we investigate a modification to the excised model it lacks the simplicity of the original excised ensemble but it serves to explain the reason for the unexpectedly low cutoff in the original excised model additionally the distribution of central l values is choppier than the distribution of characteristic polynomials in the sense that it is a superposition of a series of peaks the characteristic polynomial distribution is a smooth approximation to this the excised model did not attempt to incorporate these successive peaks only the initial cutoff here we experiment with including some of the structure of the l value distribution the conclusion is that a critical feature of a good model is to associate the correct mass to the first peak of the l value distribution

heegner divisors l functions and harmonic weak maass forms recent works mostly related to ramanujan s mock theta functions make use of the fact that harmonic weak maass forms can be combinatorial generating functions generalizing works of waldspurger kohnen and zagier we prove that such forms also serve as generating functions for central values and derivatives of quadratic twists of weight 2 modular l functions to obtain these results we construct differentials of the third kind with twisted heegner divisor by suitably generalizing the borcherds lift to harmonic weak maass forms the connection with periods fourier coefficients derivatives of l functions and points in the jacobian of modular curves is obtained by analyzing the properties of these differentials using works of scholl waldschmidt and gross and zagier