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  - 
TY  - JOUR
A1  - Steuding, Jörn
A1  - Tongsomporn, Janyarak
T1  - On the order of growth of Lerch zeta functions
JF  - Mathematics
N2  - We extend Bourgain’s bound for the order of growth of the Riemann zeta function on the critical line to Lerch zeta functions. More precisely, we prove L(λ, α, 1/2 + it) ≪ t\(^{13/84+ϵ}\) as t → ∞. For both, the Riemann zeta function as well as for the more general Lerch zeta function, it is conjectured that the right-hand side can be replaced by t\(^ϵ\) (which is the so-called Lindelöf hypothesis). The growth of an analytic function is closely related to the distribution of its zeros.
KW  - Lerch zeta function
KW  - Hurwitz zeta function
KW  - (approximate) functional equation
KW  - order of growth
KW  - exponent pairs
KW  - MSC 11M35
Y1  - 2023
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:20-opus-303981
SN  - 2227-7390
VL  - 11
IS  - 3
ER  -