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

Richard P. Brent; David J. Platt; Timothy S. Trudgian

doi:10.1090/mcom/3652

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arXiv · 2009.13791

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

Richard P. Brent·David J. Platt·Timothy S. Trudgian

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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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BibTeX RIS

Richard P. Brent, David J. Platt, Timothy S. Trudgian. 2020-09-29. Accurate estimation of sums over zeros of the Riemann zeta-function. https://doi.org/10.1090/mcom%2F3652

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