On the Random Wave Conjecture for Dihedral Maaß Forms

Peter Humphries, Rizwanur Khan

Research output: Contribution to journalArticle


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.

Original languageEnglish
JournalGeometric and Functional Analysis
Publication statusAccepted/In press - 1 Jan 2020


ASJC Scopus subject areas

  • Analysis
  • Geometry and Topology

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