Accurate Estimation Of Sums Over Zeros Of The Riemann Zeta-Function

We consider sums of the form Sigma phi(gamma), where phi 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.