On the Random Wave Conjecture for Dihedral Maaß Forms

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.

67 pages