Let $\gamma$ denote the imaginary parts of complex zeros $\rho = \beta+i\gamma$ of $\zeta(s)$. The problem of analytic continuation of the function $G(s) := \sum\limits_{ \gamma > 0}\gamma^{ -s}$ 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.
Categories: math.NT