# On the Random Wave Conjecture for Dihedral Maa{\ss} Forms

## TL;DR

This paper proves results related to quantum chaos for dihedral Maass forms, including mass equidistribution and fourth moment asymptotics, advancing understanding of Berry's conjecture in this context.

## Contribution

It establishes unconditionally the Planck scale mass equidistribution and fourth moment asymptotics for dihedral Maass forms, extending previous results known only for Eisenstein series or under hypotheses.

## Key findings

- Proves Planck scale mass equidistribution for dihedral Maass forms.
- Derives an asymptotic formula for the fourth moment of these forms.
- Provides bounds for mixed moments of L-functions implying hybrid subconvexity.

## Abstract

We prove two results on arithmetic quantum chaos for dihedral Maass forms, both of which are manifestations of Berry's random wave conjecture: Planck scale mass equidistribution and an asymptotic formula for the fourth moment. For level $1$ forms, these results were previously known for Eisenstein series and conditionally on the generalised Lindelof hypothesis for Hecke-Maass eigenforms. A key aspect of the proofs is bounds for certain mixed moments of $L$-functions that imply hybrid subconvexity.