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.

13 pages

Cited by in corpus (1)

• On sums of squares of the Riemann zeta-function on the critical line