The Values of the Periodic Zeta-Function at the Nontrivial Zeros of Riemann’s Zeta-Function

Symmetry

Jörn Steuding¹  Saeree Wananiyakul²  Janyarak Tongsomporn² 

[1] Department of Mathematics, Würzburg University, Am Hubland, 97218 Würzburg, Germany;School of Science, Walailak University, Nakhon Si Thammarat 80160, Thailand;

关键词: zeta-functions;    Riemann hypothesis;   

DOI  :  10.3390/sym13122410

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown