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SUM OF VALUES OF THE IDEAL CLASS ZETA-FUNCTION OVER NONTRIVIAL ZEROS OF THE RIEMANN ZETA-FUNCTION

Part of: Algebraic number theory: global fields Zeta and $L$-functions: analytic theory

Published online by Cambridge University Press:  31 July 2023

SAEREE WANANIYAKUL Open the ORCID record for SAEREE WANANIYAKUL [Opens in a new window] ,
JÖRN STEUDING  and
NITHI RUNGTANAPIROM Open the ORCID record for NITHI RUNGTANAPIROM [Opens in a new window]
SAEREE WANANIYAKUL
Affiliation:
Department of Mathematics and Computer Science, Faculty of Science, Chulalongkorn University, Bangkok 10330, Thailand e-mail: s.wananiyakul@hotmail.com
JÖRN STEUDING
Affiliation:
Department of Mathematics, Würzburg University, Am Hubland, Würzburg 97218, Germany e-mail: steuding@mathematik.uni-wuerzburg.de
NITHI RUNGTANAPIROM*
Affiliation:
Department of Mathematics and Computer Science, Faculty of Science, Chulalongkorn University, Bangkok 10330, Thailand
*
e-mail: nithi.r@chula.ac.th
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Abstract

We prove an upper bound for the sum of values of the ideal class zeta-function over nontrivial zeros of the Riemann zeta-function. The same result for the Dedekind zeta-function is also obtained. This may shed light on some unproved cases of the general Dedekind conjecture.

Keywords

Dedekind’s conjecturenontrivial zeros of Riemann zeta-functionzeta-function

MSC classification

Primary: 11R42: Zeta functions and $L$-functions of number fields
Secondary: 11M26: Nonreal zeros of $zeta (s)$ and $L(s, chi)$; Riemann and other hypotheses 11M41: Other Dirichlet series and zeta functions

Information

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 109 , Issue 2 , April 2024 , pp. 288 - 300
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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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