Elements of Automorphic Representations

TL;DR

This paper develops a practical, self-contained theory of automorphic representations within the framework of $L^2$ spaces on the quotient of PSL(2,R) by PSL(2,Z), aiming to deepen understanding of automorphic forms.

Contribution

It provides a comprehensive, accessible approach to automorphic representations specifically for the case of PSL(2,R) and PSL(2,Z), bridging theoretical concepts with practical methods.

Findings

Establishes a self-contained framework for automorphic representations.

Clarifies the structure of $L^2$ spaces on modular quotients.

Facilitates further research in automorphic forms and representation theory.

Abstract

This is an attempt at a practical and essentially self-contained theory of automorphic representations in the framework $$\hbox{$L^2(\varGamma\backslash\r{G})$ with $\r{G}=\r{PSL}(2,\B{R})$ and $\varGamma=\r{PSL}(2,\B{Z})$.}$$