Converse Theorems and L-Functions of Automorphic Forms

Yale University, New Haven CT

Investigators

Abstract

It is proposed to investigate L-functions of automorphic representations and their applications in the following contexts: lifitng from Classical Groups to GL(n); Converse Theorems for GL(n); L-funcitons for GL(n); sub-convexity results for L-functions. These are all ongoing projects. In addition there is a return to previous work on non-symmetric complex homogeneous domains. The proposal is devoted to the study of Langlans' philosopy, which is the main part of the modern number theory. We obtained, by using Converse Theorem, important results relating the problem of lifting of generic automorphic representations of the classical groups to GL(n). Our basic achivement will be the proof of the local and global Langlands' conjectures.