Joint value distribution of Hecke--Maass forms

TL;DR

This paper formulates a conjecture on the joint distribution of Hecke--Maass cusp forms and provides conditional results supporting the statistical independence of orthogonal cusp forms.

Contribution

It introduces a new conjecture on joint distribution and proves conditional results that support the independence of Hecke--Maass cusp forms.

Findings

Conditional results support statistical independence

Formulation of a new conjecture on joint distribution

Evidence for orthogonal cusp forms independence

Abstract

In this paper, we formulate a conjecture on joint distribution of Hecke--Maass cusp forms. To support our conjecture, we prove two conditional results on joint moments of two Hecke--Maass cusp forms, which confirms statistical independence of orthogonal cusp forms.