High precision computation of Riemann’s zeta function by the Riemann-Siegel formula, I

DOI10.1090/S0025-5718-2010-02426-3zbMath1228.11127arXiv2201.00342OpenAlexW2166585959MaRDI QIDQ3168733

Juan Arias de Reyna

Publication date: 19 April 2011

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2201.00342

zbMATH Keywords

Riemann's zeta functionRiemann-Siegel formulahigh precision computation

Mathematics Subject Classification ID

(zeta (s)) and (L(s, chi)) (11M06) Analytic computations (11Y35)

Related Items (13)

High precision computation of Riemann’s zeta function by the Riemann-Siegel formula, I ⋮ An explicit upper bound for \(|\zeta (1 + i t)|\) ⋮ Computational Number Theory, Past, Present, and Future ⋮ A fast algorithm to compute \(L(1/2, f\times \chi_q)\) ⋮ Explicit zero density estimate for the Riemann zeta-function near the critical line ⋮ Explicit bounds on \(\zeta (s)\) in the critical strip and a zero-free region ⋮ Differential calculus for linear operators represented by finite signed measures and applications ⋮ Isolating some non-trivial zeros of zeta ⋮ Series with Binomial-Like Coefficients for Evaluation and 3D Visualization of Zeta Functions ⋮ An alternative to Riemann-Siegel type formulas ⋮ Effective approximation of heat flow evolution of the Riemann \(\xi \) function, and a new upper bound for the de Bruijn-Newman constant ⋮ A generalization of the Riemann-Siegel formula ⋮ Appell-Dunkl sequences and Hurwitz-Dunkl zeta functions

Cites Work

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• High precision computation of Riemann’s zeta function by the Riemann-Siegel formula, I
• The Riemann-Siegel expansion for the zeta function: high orders and remainders
• The zeros of the Riemann zeta-function

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