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Probl. Peredachi Inf., 1995, Volume 31, Issue 4, Pages 69–80 (Mi ppi294)  

This article is cited in 8 scientific papers (total in 8 papers)

Automata Theory

Fast Calculation of the Riemann Zeta Function $\zeta(s)$ for Integer Values of the Argument $s$

E. A. Karatsuba


Abstract: We suggest an algorithm for fast calculation of the Riemann zeta function for integer values of the argument, which is based on the method for fast calculation of Siegel's $E$-functions. The computational complexity is near to optimal.

Full text: PDF file (767 kB)

English version:
Problems of Information Transmission, 1995, 31:4, 353–362

Bibliographic databases:

UDC: 621.391.1
Received: 14.03.1995

Citation: E. A. Karatsuba, “Fast Calculation of the Riemann Zeta Function $\zeta(s)$ for Integer Values of the Argument $s$”, Probl. Peredachi Inf., 31:4 (1995), 69–80; Problems Inform. Transmission, 31:4 (1995), 353–362

Citation in format AMSBIB
\Bibitem{Kar95}
\by E.~A.~Karatsuba
\paper Fast Calculation of the Riemann Zeta Function~$\zeta(s)$ for Integer Values of the Argument~$s$
\jour Probl. Peredachi Inf.
\yr 1995
\vol 31
\issue 4
\pages 69--80
\mathnet{http://mi.mathnet.ru/ppi294}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1367927}
\zmath{https://zbmath.org/?q=an:0895.11032|0859.11050}
\transl
\jour Problems Inform. Transmission
\yr 1995
\vol 31
\issue 4
\pages 353--362


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. E. A. Karatsuba, “Fast Evaluation of the Hurwitz Zeta Function and Dirichlet $L$-Series”, Problems Inform. Transmission, 34:4 (1998), 342–353  mathnet  mathscinet  zmath
    2. Karatsuba E.A., “Fast computation of (3) and of some special integrals using the Ramanujan formula and polylogarithms”, BIT, 41:4 (2001), 722–730  crossref  isi
    3. W. V. Zudilin, “A Third-Order Apéry-Like Recursion for $\zeta (5)$”, Math. Notes, 72:5 (2002), 733–737  mathnet  crossref  crossref  mathscinet  zmath  isi
    4. S. V. Yakhontov, “Effektivnoe po vremeni i pamyati vychislenie logarifmicheskoi funktsii veschestvennogo argumenta na mashine Shenkhage”, PDM, 2013, no. 2(20), 101–114  mathnet
    5. E. A. Karatsuba, “Fast Catalan constant computation via the approximations obtained by the Kummer's type transformations”, Discrete Math. Appl., 23:5-6 (2013), 429–443  mathnet  crossref  crossref  mathscinet  elib
    6. E. A. Karatsuba, “On one method for fast approximation of zeta constants by rational fractions”, Problems Inform. Transmission, 50:2 (2014), 186–202  mathnet  crossref  isi  elib
    7. E. A. Karatsuba, “On One method for constructing a family of approximations of zeta constants by rational fractions”, Problems Inform. Transmission, 51:4 (2015), 378–390  mathnet  crossref  isi  elib
    8. Karatsuba E.A., “Fast Approximations of Certain Number-Theoretic Constants”, Dokl. Math., 91:3 (2015), 283–286  crossref  isi  elib
  • Проблемы передачи информации Problems of Information Transmission
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