On a Rankin-Selberg L-Function over Different Fields

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...

Rankin-selberg L-functions and Cycles on Unitary Shimura Varieties

A Standard Zero Free Region for Rankin Selberg L-functions

A standard zero free region is obtained for Rankin Selberg L-functions L(s, f×f) where f is a tempered Maass form on GL(n) and f is not necessarily self dual. The method is based on the theory of Eisenstein series generalizing a work of Sarnak. §

Archimedean Rankin-Selberg Integrals

The paper gives complete proofs of the properties of the RankinSelberg integrals for the group GL(n,R) and GL(n,C).