Certain Rankin-Selberg integral for unitary groups

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...

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

On certain Rankin - Selberg integrals on GE 6 ∗

In this paper we begin the study of two Rankin-Selberg integrals defined on the exceptional group of type GE6. We show that each factorizes and that the contribution from the unramified places is, in one case, the degree 54 Euler product LS(π× τ, E6× GL2, s) and in the other case the degree 30 Euler product L S(π × τ,∧2 ×GL2, s).

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).

Basic Rankin-selberg

We present the simplest possible example of the Rankin-Selberg method, namely for a pair of holomorphic modular forms for SL(2,Z), treated independently in 1939 by Rankin and 1940 by Selberg. (Rankin has remarked that the general idea came from his advisor and mentor, Ingham.) We also recall a proof of the analytic continuation of the relevant Eisenstein series. That is, we consider the simples...