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On moments of L-functions over Dirichlet characters

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

Published online by Cambridge University Press:  19 September 2025

Avery Bainbridge ,
Rizwanur Khan  and
Ze Sen Tang
Avery Bainbridge
Affiliation:
Department of Mathematical Sciences, University of Texas at Dallas , Richardson, TX 75080, United States e-mail: Avery.Bainbridge@UTDallas.edu ZeSen.Tang@UTDallas.edu
Rizwanur Khan*
Affiliation:
Department of Mathematical Sciences, University of Texas at Dallas , Richardson, TX 75080, United States e-mail: Avery.Bainbridge@UTDallas.edu ZeSen.Tang@UTDallas.edu
Ze Sen Tang
Affiliation:
Department of Mathematical Sciences, University of Texas at Dallas , Richardson, TX 75080, United States e-mail: Avery.Bainbridge@UTDallas.edu ZeSen.Tang@UTDallas.edu
*
e-mail: Rizwanur.Khan@UTDallas.edu
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Abstract

We give a new proof of Heath-Brown’s full asymptotic expansion for the second moment of Dirichlet L-functions and we obtain a corresponding asymptotic expansion for a twisted first moment of Hecke–Maass L-functions.

Keywords

Dirichlet L-functionsmomentsstationary phase

MSC classification

Primary: 11M06: $zeta (s)$ and $L(s, chi)$ 11F11: Holomorphic modular forms of integral weight

Information

Type
Article
Information
Canadian Mathematical Bulletin , First View , pp. 1 - 24
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of Canadian Mathematical Society

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Footnotes

The second and third authors were supported by the National Science Foundation grants DMS-2344044 and DMS-2341239.

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