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The fifth moment of Hecke L-functions in the weight aspect

Part of: Zeta and $L$-functions: analytic theory Discontinuous groups and automorphic forms

Published online by Cambridge University Press:  14 January 2019

RIZWANUR KHAN
RIZWANUR KHAN*
Affiliation:
Department of Mathematics, University of Mississippi, University, MS 38677-1848, U.S.A.
*
e-mails: rrkhan@olemiss.edu
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Abstract

We prove an upper bound for the fifth moment of Hecke L-functions associated to holomorphic Hecke cusp forms of full level and weight k in a dyadic interval K ≤ k ≤2K, as K → ∞. The bound is sharp on Selberg’s eigenvalue conjecture.

MSC classification

Primary: 11F03: Modular and automorphic functions
Secondary: 11M99: None of the above, but in this section
Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 168 , Issue 3 , May 2020 , pp. 543 - 566
Copyright
Copyright © Cambridge Philosophical Society 2019

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