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On the fourth moment of Hecke–Maass forms and the random wave conjecture

Part of: Discontinuous groups and automorphic forms General mathematical topics and methods in quantum theory Zeta and $L$-functions: analytic theory

Published online by Cambridge University Press:  02 May 2017

Jack Buttcane  and
Rizwanur Khan
Jack Buttcane
Affiliation:
Mathematics Department, 244 Mathematics Building, University at Buffalo, Buffalo, NY 14260, USA email buttcane@buffalo.edu
Rizwanur Khan
Affiliation:
Science Program, Texas A&M University at Qatar, PO Box 23874, Doha, Qatar email rizwanur.khan@qatar.tamu.edu
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Abstract

Conditionally on the generalized Lindelöf hypothesis, we obtain an asymptotic for the fourth moment of Hecke–Maass cusp forms of large Laplacian eigenvalue for the full modular group. This lends support to the random wave conjecture.

Keywords

L-functionsautomorphic formsL 4 -normquantum chaosrandom wave conjecture

MSC classification

Primary: 11F12: Automorphic forms, one variable 11M99: None of the above, but in this section
Secondary: 81Q50: Quantum chaos

Information

Type
Research Article
Information
Compositio Mathematica , Volume 153 , Issue 7 , July 2017 , pp. 1479 - 1511
Copyright
© The Authors 2017 

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