The Values of the Periodic Zeta-Function at the Nontrivial Zeros of Riemann’s Zeta-Function
Keyword(s):
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.
QUESTIONS AROUND THE NONTRIVIAL ZEROS OF THE RIEMANN ZETA-FUNCTION. COMPUTATIONS AND CLASSIFICATIONS
2011 ◽
Vol 16
(1)
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pp. 72-81
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2016 ◽
Vol 162
(2)
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pp. 293-317
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2017 ◽
2017 ◽
Keyword(s):