On Riesz mean for the coefficients of twisted Rankin-Selberg L-functions

Nonvanishing of certain Rankin-Selberg L-functions

In this article we prove that given a holomorphic cusp form f and any point s0 in the complex plane, there is a holomorphic cusp form g such that the Rankin-Selberg L-function L(s, f × g) is non-zero at s0. Résumé: Dans cet article, on prouve le résultat suivant. Etat donné une forme holomorphe cuspidale f et un point quelquonque du plan complexe, il existe une forme holomorphe cuspidale g tell...

On the Exceptional Zeros of Rankin-selberg L-functions

In this paper we study the possibility of real zeros near s = 1 for the RankinSelberg L-functions L(s, f × g) and L(s, sym(g) × sym(g)), where f, g are newforms, holomorphic or otherwise, on the upper half plane H, and sym(g) denotes the automorphic form on GL(3)/Q associated to g by Gelbart and Jacquet ([GJ79]). We prove that the set of such zeros of these L-functions is the union of the corre...

The central value of the Rankin-Selberg L-functions

The values of L-functions at special points have been the subject of intensive studies. For example, a good positive lower bound for the central value of Hecke L-functions would rule out the existence of the Landau-Siegel zero, see the notable paper [IS]; the nonvanishing of certain Rankin-Selberg L-functions is a crucial ingredient in the current development of the generalized Ramanujan conjec...

The Mean Values and the Universality of Rankin-Selberg L-Functions

Subconvexity for Rankin-selberg L-functions of Maass Forms

This is a joint work with Yangbo Ye. We prove a subconvexity bound for Rankin-Selberg L-functions L(s, f⊗g) associated with a Maass cusp form f and a fixed cusp form g in the aspect of the Laplace eigenvalue 1/4 + k2 of f , on the critical line Res = 1/2. Using this subconvexity bound, we prove the equidistribution conjecture of Rudnick and Sarnak on quantum unique ergodicity for dihedral Maass...