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arXiv · 1808.01763

On certain sums over ordinates of zeta-zeros II

Andriy Bondarenko·Aleksandar Ivić·Eero Saksman·Kristian Seip
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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 $G(s) := \sum\limits_{\gamma > 0}\gamma^{-s}$ 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.

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Andriy Bondarenko, Aleksandar Ivić, Eero Saksman, Kristian Seip. 2018-08-06. On certain sums over ordinates of zeta-zeros II. https://arxiv.org/abs/1808.01763

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