Joint distribution of Hecke eigenforms on $\mathbb{H}^3$

TL;DR

This paper proves a joint value equidistribution for Hecke-Maa{ ext} cusp forms on hyperbolic three-space, providing evidence for their statistical independence, which advances understanding of automorphic forms in higher dimensions.

Contribution

It establishes a joint equidistribution result for Hecke-Maa{ ext} cusp forms on $ ext{H}^3$, supporting conjectures about their independence.

Findings

Supports conjecture of statistical independence of cusp forms

Provides a new equidistribution result in hyperbolic 3-space

Advances understanding of automorphic forms in higher dimensions

Abstract

We prove a joint value equidistribution statement for Hecke-Maa{\ss} cusp forms on the hyperbolic three-space $\mathbb{H}^3$. This supports the conjectural statistical independence of orthogonal cusp forms.