Accurate estimation of sums over zeros of the Riemann zeta-function

Abstract

We consider sums of the form $\sum \varphi (\gamma )$, where $\varphi$ is a given function, and $\gamma$ ranges over the ordinates of nontrivial zeros of the Riemann zeta-function in a given interval. We show how the numerical estimation of such sums can be accelerated by a simple device, and give examples involving both convergent and divergent infinite sums.

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