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

15 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

Access to Document

10.1090/mcom/3652

Cite this

@article{649d179680ad4b9aa4622a8f4bcf42c4,

title = "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.",

author = "Brent, \{Richard P.\} and Platt, \{David J.\} and Trudgian, \{Timothy S.\}",

note = "Publisher Copyright: {\textcopyright} 2021 American Mathematical Society",

year = "2021",

doi = "10.1090/mcom/3652",

language = "English",

volume = "90",

pages = "2923--2935",

journal = "Mathematics of Computation",

issn = "0025-5718",

publisher = "American Mathematical Society",

number = "332",

}

TY - JOUR

T1 - Accurate estimation of sums over zeros of the riemann zeta-function

AU - Brent, Richard P.

AU - Platt, David J.

AU - Trudgian, Timothy S.

PY - 2021

Y1 - 2021

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.

UR - https://www.scopus.com/pages/publications/85114813136

U2 - 10.1090/mcom/3652

DO - 10.1090/mcom/3652

M3 - Article

SN - 0025-5718

VL - 90

SP - 2923

EP - 2935

JO - Mathematics of Computation

JF - Mathematics of Computation

IS - 332

ER -

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

Abstract

Access to Document

Other files and links

Fingerprint

Cite this