On certain sums over ordinates of zeta zeros

Abstract

Let $γ$ denote imaginary parts of complex zeros of the Riemann zeta-function $ζ(s)$. Certain sums over the $γ$'s are evaluated, by using the function $G(s) = \sum_{γ>0}γ^{-s}$ and other techniques. Some integrals involving the function $S(T) = (1/π)\argζ(1/2+iT)$ are also considered.