© 2020, The Author(s). 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 Lindelöf hypothesis for Hecke–Maaß eigenforms. A key aspect of the proofs is bounds for certain mixed moments of L-functions that imply hybrid subconvexity.
Humphries, P., & Khan, R. (2020). On the Random Wave Conjecture for Dihedral Maaß Forms. Geometric and Functional Analysis, 30(1), 34–125. https://doi.org/10.1007/s00039-020-00526-4