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.

arXiv comment67 pages

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Cited by in corpus (6)

• Optimal Small Scale Equidistribution of Lattice Points on the Sphere, Heegner Points, and Closed Geodesics
• Motohashi's Formula for the Fourth Moment of Individual Dirichlet $L$-Functions and Applications
• The Twelfth Moment of Hecke $L$-Functions in the Weight Aspect
• The cubic moment of Hecke--Maass cusp forms and moments of $L$-functions
• Wide moments of $L$-functions I: Twists by class group characters of imaginary quadratic fields
• $L^p$-Norm Bounds for Automorphic Forms via Spectral Reciprocity