A HARMONIC SUM OVER NONTRIVIAL ZEROS OF THE RIEMANN ZETA-FUNCTION

DOI10.1017/S0004972720001252zbMath1479.11144arXiv2009.05251OpenAlexW3109702898MaRDI QIDQ4999615

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

Publication date: 7 July 2021

Published in: Bulletin of the Australian Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2009.05251

zbMATH Keywords

nontrivial zerosRiemann zeta-functionacceleration

Mathematics Subject Classification ID

Nonreal zeros of (zeta (s)) and (L(s, chi)); Riemann and other hypotheses (11M26) Evaluation of number-theoretic constants (11Y60)

Related Items (1)

The mean square of the error term in the prime number theorem

Cites Work

• An improved upper bound for the argument of the Riemann zeta-function on the critical line. II
• Estimating $\pi (x)$ and related functions under partial RH assumptions
• Improvements to Turing’s method
• Some New Algorithms for High-Precision Computation of Euler's Constant
• On the Distribution of Spacings Between Zeros of the Zeta Function
• A bound for the error term in the Brent-McMillan algorithm
• A still sharper region where $\pi (x)-{\mathrm {li}}(x)$ is positive
• On the difference π(x) - li(x)
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