Email this article A Few Factors from the Euler Product Are Sufficient for Calculating the Zeta Function with High Precision
- Authors: Matiyasevich Y.V.1
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Affiliations:
- St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences
- Issue: Vol 299, No 1 (2017)
- Pages: 178-188
- Section: Article
- URL: https://journals.rcsi.science/0081-5438/article/view/175157
- DOI: https://doi.org/10.1134/S0081543817080120
- ID: 175157
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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).
About the authors
Yu. V. Matiyasevich
St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences
Author for correspondence.
Email: yumat@pdmi.ras.ru
Russian Federation, nab. Fontanki 27, St. Petersburg, 191023
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