Humphries, P;
Khan, R;
(2020)
On the Random Wave Conjecture for Dihedral Maaß Forms.
Geometric and Functional Analysis
, 30
(1)
pp. 34-125.
10.1007/s00039-020-00526-4.
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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 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.
| Type: | Article |
|---|---|
| Title: | On the Random Wave Conjecture for Dihedral Maaß Forms |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1007/s00039-020-00526-4 |
| Publisher version: | https://doi.org/10.1007/s00039-020-00526-4 |
| Language: | English |
| Additional information: | © 2020 Springer Nature. This article is licensed under a Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/). |
| Keywords: | 11F12 (primary), 58J51, 81Q50 (secondary) |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10101905 |
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