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arXiv · 1904.05235

On the Random Wave Conjecture for Dihedral Maaß Forms

Peter Humphries·Rizwanur Khan
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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.

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Peter Humphries, Rizwanur Khan. 2019-10-18. On the Random Wave Conjecture for Dihedral Maaß Forms. https://doi.org/10.1007/s00039-020-00526-4

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