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

Brent, Richard; Platt, David; Trudgian, Timothy

doi:10.1090/mcom/3652

Accurate estimation of sums over zeros of the Riemann zeta-function
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by Richard P. Brent, David J. Platt and Timothy S. Trudgian HTML | PDF

Math. Comp. 90 (2021), 2923-2935 Request permission

Abstract:

We consider sums of the form $\sum \phi (\gamma )$, 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.

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