On the fourth moment of Hecke Maass forms and the Random Wave Conjecture

TL;DR

This paper provides an asymptotic formula for the fourth moment of Hecke Maass cusp forms under the Generalized Lindelöf Hypothesis, supporting the Random Wave Conjecture about eigenfunctions.

Contribution

It offers the first conditional asymptotic result for the fourth moment of Hecke Maass forms, advancing understanding of their distribution.

Findings

Supports the Random Wave Conjecture

Provides asymptotic for the fourth moment under GHL hypothesis

Links eigenfunction behavior to conjectural models

Abstract

Conditionally on the Generalized Lindel\"of Hypothesis, we obtain an asymptotic for the fourth moment of Hecke Maass cusp forms of large Laplacian eigenvalue for the full modular group. This lends support to the Random Wave Conjecture.