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A Few Factors from the Euler Product Are Sufficient for Calculating the Zeta Function with High Precision

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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 ζ(1/4 + 10i).

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Authors and Affiliations

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

    Yu. V. Matiyasevich

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  1. Yu. V. Matiyasevich
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Correspondence to Yu. V. Matiyasevich.

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Published in Russian in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2017, Vol. 299, pp. 192–202.

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Matiyasevich, Y.V. A Few Factors from the Euler Product Are Sufficient for Calculating the Zeta Function with High Precision. Proc. Steklov Inst. Math. 299, 178–188 (2017). https://doi.org/10.1134/S0081543817080120

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  • DOI: https://doi.org/10.1134/S0081543817080120

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