Spectral Analysis of the Zeta and L-Functions

TL;DR

This paper discusses the application of automorphic representation theory to classical problems involving the zeta and L-functions, highlighting basic results and their significance in number theory.

Contribution

It demonstrates how automorphic representations can be applied to traditional problems in the theory of zeta and L-functions, focusing on fundamental issues.

Findings

Application of automorphic representations to zeta functions

Basic results connecting automorphic forms and L-functions

Illustration of classical problems through modern representation theory

Abstract

This is my talk delivered at the workshop 'Automorphic L-Functions and related prpblems' (March 10--13, 2012, Tokyo University). We showed an instance of applications of the theory of automorphic representations to a genuinely traditional problem in the theory of the zeta and allied functions. We restricted ourselves to very basic issues and results, because of the purpose of the workshop.