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A NOTE ON LARGE VALUES OF $\boldsymbol{L(\sigma ,\chi )}$

Part of: Zeta and $L$-functions: analytic theory

Published online by Cambridge University Press:  04 October 2021

XUANXUAN XIAO Open the ORCID record for XUANXUAN XIAO [Opens in a new window]  and
QIYU YANG Open the ORCID record for QIYU YANG [Opens in a new window]
XUANXUAN XIAO
Affiliation:
Faculty of Information Technology, Macau University of Science and Technology, Macau e-mail: xiaoxuan.uhp@gmail.com
QIYU YANG*
Affiliation:
Faculty of Information Technology, Macau University of Science and Technology, Macau
*
e-mail: qyyang.must@gmail.com
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Abstract

In this note, by introducing a new variant of the resonator function, we give an explicit version of the lower bound for $\log |L(\sigma ,\chi )|$ in the strip $1/2<\sigma <1$ , which improves the result of Aistleitner et al. [‘On large values of $L(\sigma ,\chi )$ ’, Q. J. Math. 70 (2019), 831–848].

Keywords

large valueDirichlet L-functionresonance method

MSC classification

Primary: 11M06: $zeta (s)$ and $L(s, chi)$
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 105 , Issue 3 , June 2022 , pp. 412 - 418
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Copyright
© The Author(s), 2021. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.

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Footnotes

This work is supported by the Science and Technology Development Fund, Macau SAR (File no. 0095/2018/A3).

References

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