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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2017, Volume 299, Pages 192–202
DOI: https://doi.org/10.1134/S0371968517040124 (Mi tm3831) 		 
This article is cited in 2 scientific papers (total 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
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DOI: https://doi.org/10.1134/S0371968517040124
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.
Funding agency Grant number
Russian Academy of Sciences - Federal Agency for Scientific Organizations
Received: January 30, 2017
English version:
Proceedings of the Steklov Institute of Mathematics, 2017, Volume 299, Pages 178–188
DOI: https://doi.org/10.1134/S0081543817080120
Bibliographic databases:
Document Type: Article
UDC: 511.331
Language: Russian
Citation: Yu. V. Matiyasevich, “A few factors from the Euler product are sufficient for calculating the zeta function with high precision”, Analytic number theory, On the occasion of the 80th anniversary of the birth of Anatolii Alekseevich Karatsuba, Trudy Mat. Inst. Steklova, 299, MAIK Nauka/Interperiodica, Moscow, 2017, 192–202; Proc. Steklov Inst. Math., 299 (2017), 178–188
Citation in format AMSBIB
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\paper A few factors from the Euler product are sufficient for calculating the zeta function with high precision
\inbook Analytic number theory
\bookinfo On the occasion of the 80th anniversary of the birth of Anatolii Alekseevich Karatsuba
\serial Trudy Mat. Inst. Steklova
\yr 2017
\vol 299
\pages 192--202
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
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\crossref{https://doi.org/10.1134/S0371968517040124}
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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