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

Abstract

We consider sums of the form Σφ(γ), where φ is a given function, and γ 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. Show more