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JOURNALS // Trudy Matematicheskogo Instituta imeni V.A. Steklova // Archive

Trudy Mat. Inst. Steklova, 2017 Volume 299, Pages 192–202 (Mi tm3831)

This article is cited in 2 papers

A few factors from the Euler product are sufficient for calculating the zeta function with high precision

Yu. V. Matiyasevich

St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences, nab. Fontanki 27, St. Petersburg, 191023 Russia

Abstract: The paper demonstrates by numerical examples a nontraditional way to get high precision values of Riemann's zeta function inside the critical strip by using the functional equation and the factors from the Euler product corresponding to a very small number of primes. For example, the three initial primes produce more than 50 correct decimal digits of $\zeta (1/4+10\kern 1pt\mathrm i)$.

Keywords: Riemann's zeta function, functional equation, Euler product.

UDC: 511.331

Received: January 30, 2017

DOI: 10.1134/S0371968517040124


 English version:
Proceedings of the Steklov Institute of Mathematics, 2017, 299, 178–188

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© Steklov Math. Inst. of RAS, 2024