On the Random Wave Conjecture for Eisenstein series

TL;DR

This paper proves an asymptotic result for the fourth moment of Eisenstein series, supporting the Random Wave Conjecture for the full modular group, and providing evidence for the conjecture's validity.

Contribution

It provides the first asymptotic for the regularized fourth moment of Eisenstein series, confirming predictions of the Random Wave Conjecture.

Findings

Asymptotic formula for the regularized fourth moment

Supports the validity of the Random Wave Conjecture

Advances understanding of Eisenstein series behavior

Abstract

We obtain an asymptotic for the regularized fourth moment of the Eisenstein series for the full modular group, in agreement with the Random Wave Conjecture.