Bounds for moments of cubic and quartic Dirichlet L-functions

We study the 2k-th moment of central values of the family of primitive cubic and quartic Dirichlet L-functions. We establish sharp lower bounds for all real k≥1/2 unconditionally for the cubic case and under the Lindelöf hypothesis for the quartic case. We also establish sharp lower bounds for all r...

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Bibliographic Details
Published in:Indagationes mathematicae 2022-11, Vol.33 (6), p.1263-1296
Main Authors: Gao, Peng, Zhao, Liangyi
Format: Article
Language:English
Subjects:
Cubic Dirichlet L-functions
Lower bounds
Moments
Quartic Dirichlet L-functions
Upper bounds
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Summary:We study the 2k-th moment of central values of the family of primitive cubic and quartic Dirichlet L-functions. We establish sharp lower bounds for all real k≥1/2 unconditionally for the cubic case and under the Lindelöf hypothesis for the quartic case. We also establish sharp lower bounds for all real 0≤k
ISSN:0019-3577
1872-6100
DOI:10.1016/j.indag.2022.08.003