Some perspectives on Eisenstein series

TL;DR

This paper reviews key topics in the analytic theory of Eisenstein series, including their meromorphic continuation, spectral expansion, and Fourier coefficients, while also highlighting open problems in the field.

Contribution

It provides a comprehensive overview of recent developments and open questions in the analytic theory of Eisenstein series.

Findings

Analysis of meromorphic continuation of Eisenstein series

Spectral expansion techniques for Eisenstein series

Discussion of open problems in the field

Abstract

We review some topics in the analytic theory of Eisenstein series, including meromorphic continuation, $L^2$-spectral expansion and Fourier coefficients. We also discuss some open problems.