The values of the periodic zeta-function at the nontrivial zeros of Riemann's zeta-function

Please always quote using this URN: urn:nbn:de:bvb:20-opus-252261
  • In this paper, we prove an asymptotic formula for the sum of the values of the periodic zeta-function at the nontrivial zeros of the Riemann zeta-function (up to some height) which are symmetrical on the real line and the critical line. This is an extension of the previous results due to Garunkštis, Kalpokas, and, more recently, Sowa. Whereas Sowa's approach was assuming the yet unproved Riemann hypothesis, our result holds unconditionally.

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Author: Janyarak Tongsomporn, Saeree Wananiyakul, Jörn Steuding
Document Type:Journal article
Faculties:Fakultät für Mathematik und Informatik / Institut für Mathematik
Parent Title (English):Symmetry
Year of Completion:2021
Article Number:2410
Source:Symmetry (2021) 13:12, 2410.
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
Tag:Riemann hypothesis; zeta-functions
Release Date:2022/12/14
Date of first Publication:2021/12/13
Licence (German):License LogoCC BY: Creative-Commons-Lizenz: Namensnennung 4.0 International