On certain sums over ordinates of zeta zeros

Abstract

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