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A NOTE ON THE LARGE VALUES OF $|\zeta ^{(\ell )}(1+{i}t)|$

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

Published online by Cambridge University Press:  05 January 2023

ZIKANG DONG Open the ORCID record for ZIKANG DONG [Opens in a new window]  and
BIN WEI Open the ORCID record for BIN WEI [Opens in a new window]
ZIKANG DONG
Affiliation:
CNRS LAMA 8050, Laboratoire d’analyse et de mathématiques appliquées, Université Paris-Est Créteil, 61 avenue du Général de Gaulle, 94010 Créteil Cedex, France e-mail: zikangdong@gmail.com
BIN WEI*
Affiliation:
Center for Applied Mathematics, Tianjin University, Tianjin 300072, PR China
*
e-mail: bwei@tju.edu.cn
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Abstract

We investigate the large values of the derivatives of the Riemann zeta function $\zeta (s)$ on the 1-line. We give a larger lower bound for $\max _{t\in [T,2T]}|\zeta ^{(\ell )}(1+{i} t)|$, which improves the previous result established by Yang [‘Extreme values of derivatives of the Riemann zeta function’, Mathematika 68 (2022), 486–510].

Keywords

extreme valuesRiemann zeta function

MSC classification

Primary: 11M06: $zeta (s)$ and $L(s, chi)$
Secondary: 11N37: Asymptotic results on arithmetic functions

Information

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 108 , Issue 2 , October 2023 , pp. 217 - 223
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Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.

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Footnotes

The first author is supported by the China Scholarship Council (CSC) for his study in France. The second author is supported by Natural Science Foundation of Tianjin City (Grant No. 19JCQNJC14200).

References

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