Approximation of Riemann’s Zeta Function by Finite Dirichlet Series: A Multiprecision Numerical Approach

DOI10.1080/10586458.2014.976801zbMath1381.11075arXiv1402.5295OpenAlexW2000649349MaRDI QIDQ5264648

Gleb Beliakov, Yu. V. Matiyasevich

Publication date: 27 July 2015

Published in: Experimental Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1402.5295

zbMATH Keywords

\(L\)-functionzeta functionRiemann hypothesis

Mathematics Subject Classification ID

(zeta (s)) and (L(s, chi)) (11M06) Computation of special functions and constants, construction of tables (65D20) Numerical computation of determinants (65F40) Nonreal zeros of (zeta (s)) and (L(s, chi)); Riemann and other hypotheses (11M26)

Related Items (10)

A parallel algorithm for calculation of determinants and minors using arbitrary precision arithmetic ⋮ Calculation of the values of the Riemann zeta function via values of its derivatives at a single point ⋮ Towards non-iterative calculation of the zeros of the Riemann zeta function ⋮ Fractional calculus in abstract space and its application in fractional Dirichlet type problems ⋮ Computational Aspects of Hamburger’s Theorem ⋮ Continuous crop circles drawn by Riemann's zeta function ⋮ Riemann’s zeta function and finite Dirichlet series ⋮ On the fast Lanczos method for computation of eigenvalues of Hankel matrices using multiprecision arithmetics ⋮ Plausible ways for calculating the Riemann zeta function via the Riemann-Siegel theta function ⋮ Discretized Keiper/Li Approach to the Riemann Hypothesis

Cites Work

• About the infimum of the real parts of the zeros of the partial sums of the Riemann zeta-function
• Computational strategies for the Riemann zeta function
• Zeros of the Davenport-Heilbronn counterexample
• Zeros of Partial Sums of the Riemann Zeta Function
• Asymptotic Formula for the Coordinates of the Zeros of Sections of the Zeta Function, ζ _N ( s ), Near s = 1
• On the Zeros of Certain Dirichlet Series

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