Sum of the periodic zeta-function over the nontrivial zeros of the Riemann zeta-function

摘要

We consider the asymptotic of the sum of values of the periodic zeta-function L(s, λ) over nontrivial zeros of the Riemann zeta-function ζ (s). J. Steuding for rational λ obtained the main term. Assuming the Generalized Riemann Hypothesis we calculate the next term.