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Shifted moments of quadratic Dirichlet L-functions

Part of: Exponential sums and character sums Zeta and $L$-functions: analytic theory

Published online by Cambridge University Press:  24 March 2025

Peng Gao Open the ORCID record for Peng Gao [Opens in a new window]  and
Liangyi Zhao Open the ORCID record for Liangyi Zhao [Opens in a new window]
Peng Gao
Affiliation:
School of Mathematical Sciences, Beihang University, Beijing, 100191, China e-mail: [email protected]
Liangyi Zhao*
Affiliation:
School of Mathematics and Statistics, University of New South Wales, Sydney, NSW, 2052, Australia
*
e-mail: [email protected]
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Abstract

We establish sharp upper bounds for shifted moments of quadratic Dirichlet L-function under the generalized Riemann hypothesis. Our result is then used to prove bounds for moments of quadratic Dirichlet character sums.

Keywords

Quadratic Dirichlet charactersquadratic Dirichlet L-functionsshifted moments

MSC classification

Primary: 11L40: Estimates on character sums 11M06: $zeta (s)$ and $L(s, chi)$
Type
Article
Information
Canadian Mathematical Bulletin , First View , pp. 1 - 28
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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

P. G. is supported in part by NSFC grant 12471003 and L. Z. by the FRG Grant PS71536 at the University of New South Wales.

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