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

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

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

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

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

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

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

management of surgical waiting lists through a possibilistic linear multiobjective programming problem this study attempts to apply a management science technique to improve the efficiency of hospital administration we aim to design the performance of the surgical services at a public hospital that allows the decision maker to plan surgical scheduling over one year in order to reduce waiting lists real decision problems usually involve several objectives that have parameters which are often given by the decision maker in an imprecise way it is possible to handle these kinds of problems through multiple criteria models in terms of possibility theory here we apply a possibilistic linear multiobjective programming method developed by the authors for solving a hospital management problem using a fuzzy compromise programming approach