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

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

Richard P. Brent^*, David J. Platt, Timothy S. Trudgian

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

12 Citations (Scopus)

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.

Original language	English
Pages (from-to)	2923-2935
Number of pages	13
Journal	Mathematics of Computation
Volume	90
Issue number	332
DOIs	https://doi.org/10.1090/mcom/3652
Publication status	Published - 2021

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10.1090/mcom/3652

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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.",

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AU - Brent, Richard P.

AU - Platt, David J.

AU - Trudgian, Timothy S.

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N2 - 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.

AB - 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.

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U2 - 10.1090/mcom/3652

DO - 10.1090/mcom/3652

M3 - Article

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VL - 90

SP - 2923

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JO - Mathematics of Computation

JF - Mathematics of Computation

IS - 332

ER -

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

Abstract

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