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BOUNDS FOR MOMENTS OF QUADRATIC DIRICHLET CHARACTER SUMS

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

Published online by Cambridge University Press:  06 May 2024

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, PR China e-mail: penggao@buaa.edu.cn
LIANGYI ZHAO*
Affiliation:
School of Mathematics and Statistics, University of New South Wales, Sydney, NSW 2052, Australia
*
e-mail: l.zhao@unsw.edu.au
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Abstract

We establish upper bounds for moments of smoothed quadratic Dirichlet character sums under the generalized Riemann hypothesis, confirming a conjecture of M. Jutila [‘On sums of real characters’, Tr. Mat. Inst. Steklova 132 (1973), 247–250].

Keywords

quadratic Dirichlet charactermoments

MSC classification

Primary: 11L40: Estimates on character sums
Secondary: 11M06: $zeta (s)$ and $L(s, chi)$

Information

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 111 , Issue 1 , February 2025 , pp. 43 - 47
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Copyright
© The Author(s), 2024. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.

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Footnotes

The first author is supported in part by NSFC grant no. 11871082 and the second author by the FRG Grant PS71536 at the University of New South Wales.

References

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