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math.NT2019
On primeness of the Selberg zeta-function
Ramūnas Garunkštis, Jörn Steuding
In this note we prove that the Selberg zeta-function associated to a compact Riemann surface is pseudo-prime and right-prime in the sense of a decomposition.
math.NT2019
Zeros of the extended Selberg class zeta-functions and of their derivatives
Ramūnas Garunkštis
Levinson and Montgomery proved that the Riemann zeta-function and its derivative have approximately the same number of non-real zeros left of the critical line. R. Spira sho…
math.NT2019★ 1 cited
Zeros of the Lerch zeta-function and of its derivative for equal parameters
Ramūnas Garunkštis, Rokas Tamošiūnas
A. Speiser proved that the Riemann hypothesis is equivalent to the absence of non-real zeros of the derivative of the Riemann zeta-function left of the critical line. His result ha…