Proceedings of the Steklov Institute of Mathematics

, Volume 299, Issue 1, pp 178–188 | Cite as

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

  • Yu. V. Matiyasevich


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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Copyright information

© Pleiades Publishing, Ltd. 2017

Authors and Affiliations

  1. 1.St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of SciencesSt. PetersburgRussia

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