TY  - JOUR
A1  - Tongsomporn, Janyarak
A1  - Wananiyakul, Saeree
A1  - Steuding, Jörn
T1  - The values of the periodic zeta-function at the nontrivial zeros of Riemann's zeta-function
JF  - Symmetry
N2  - 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.
KW  - zeta-functions
KW  - Riemann hypothesis
Y1  - 2021
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:20-opus-252261
SN  - 2073-8994
VL  - 13
IS  - 12
ER  -