We consider the lacunary Dirichlet series obtained by taking the reciprocals of the s-th powers of the Fibonacci numbers. This series admits an analytic continuation to the entire complex plane. Its special values at integral arguments are then studied. If the argument is a negative integer, the value is algebraic. If the argument is a positive even integer, the value is transcendental by Neste...

Keywords: Hurwitz–Lerch Zeta function Lipschitz–Lerch Zeta function Lerch Zeta function Hurwitz Zeta function Riemann Zeta function Legendre chi function Bernoulli polynomials Bernoulli numbers Discrete Fourier transform a b s t r a c t It is shown that there exists a companion formula to Srivastava's formula for the Lipschitz–Lerch Zeta function [see H.M. Srivastava, Some formulas for the Bern...

In this paper, we prove an asymptotic formula for the sum of values periodic zeta-function at nontrivial zeros Riemann (up to some height) which are symmetrical on real line and critical line. This is extension previous results due Garunkštis, Kalpokas, and, more recently, Sowa. Whereas Sowa’s approach was assuming yet unproved hypothesis, our result holds unconditionally.