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

This article is cited in 5 scientific papers (total in 5 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 (in Russian): 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

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{http://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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  • http://mi.mathnet.ru/eng/ppi/v31/i4/p69

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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. Е. А. Карацуба, “Быстрое вычисление значений дзета-функции Гурвица и $L$-рядов Дирихле”, Пробл. передачи информ., 34:4 (1998), 62–75  mathnet  mathscinet  zmath; E. A. Karatsuba, “Fast Evaluation of the Hurwitz Zeta Function and Dirichlet $L$-Series”, Problems Inform. Transmission, 34:4 (1998), 342–353
    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
    3. В. В. Зудилин, “О рекурсии третьего порядка типа Апери для $\zeta(5)$”, Матем. заметки, 72:5 (2002), 796–800  mathnet  crossref  mathscinet  zmath; W. V. Zudilin, “A Third-Order Apéry-Like Recursion for $\zeta (5)$”, Math. Notes, 72:5 (2002), 733–737  crossref
    4. С. В. Яхонтов, “Эффективное по времени и памяти вычисление логарифмической функции вещественного аргумента на машине Шëнхаге”, ПДМ, 2013, № 2, 101–114  mathnet
    5. Е. А. Карацуба, “Быстрое вычисление константы Каталана через приближения, полученные преобразованиями типа куммеровских”, Дискрет. матем., 25:4 (2013), 74–87  mathnet  crossref; 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  crossref
  • Проблемы передачи информации Problems of Information Transmission
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