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The fourth moment of Dirichlet L-functions along the critical line

  • Xiaosheng Wu EMAIL logo
Published/Copyright: July 26, 2023

Abstract

For a positive integer q 2 ( mod 4 ) , this work considers the fourth moment of Dirichlet L-functions averaged over both t [ 0 , T ] and primitive characters modulo q. An asymptotic formula with a power saving from both the q-aspect and the t-aspect in the error term is obtained.

MSC 2020: 11M06

Communicated by Chantal David


Award Identifier / Grant number: 12271135

Award Identifier / Grant number: 11871187

Award Identifier / Grant number: PA2021KCPY0040

Funding statement: This work is supported in part by the National Natural Science Foundation of China (Grant nos. 12271135, 11871187) and the Fundamental Research Funds for the Central Universities of China.

Acknowledgements

The author would like to express our heartfelt thanks to the anonymous referees for their careful reading and helpful suggestion.

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Received: 2022-10-19
Revised: 2023-03-09
Published Online: 2023-07-26
Published in Print: 2023-09-01

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