On certain sums over ordinates of zeta-zeros II

Abstract

Let $\gamma$ denote the imaginary parts of complex zeros $\rho =\beta +i\gamma$ of $\zeta (s)$. The problem of analytic continuation of the function $G(s):=\sum _{\gamma >0}{\gamma }^{-s}$ to the left of the line $\Re s=-1$ is investigated, and its Laurent expansion at the pole $s=1$ is obtained. Estimates for the second moment on the critical line ${\int }_1^T|G(1/2+it){|}^{2}dt$ are revisited. This paper is a continuation of work begun by the second author in 2001.

arXiv comment12 pages