Integrals of automorphic forms and L-functions

Abstract

This Thesis consists of two topics. The first topic (Chapter 2) is about extending the $GL_ntimes GL_{n-1}$ Rankin-Selberg integral to certain cases that the automorphic forms that are involved are relative rank one Eisenstein series. The main result is an expression of the residues as $GL_{n-1}\times GL_{n-2}$ Rankin-Selberg integrals for cusp forms. The other topic (Chapter 3) is about symplectic integrals of cusp forms on GL(2n). The main result is a generalization of the Rankin-Selberg integral representing the exterior cube L-function on GL(6). At this moment we cannot extract any information for L-functions from this identity. We hope that this will be possible in the future.