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Probl. Peredachi Inf., 1998, Volume 34, Issue 4, Pages 62–75 (Mi ppi425)  

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

Automata Theory

Fast Evaluation of the Hurwitz Zeta Function and Dirichlet $L$-Series

E. A. Karatsuba


Abstract: Based on the FEE method, an algorithm of fast evaluation of the Hurwitz zeta function $\zeta(s,a)$ for integer $s$ and algebraic $a$ is proposed. Fast evaluation of Dirichlet $L$-series is considered. The evaluation complexity is close to the best possible.

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References (in Russian): PDF file   HTML файл

English version:
Problems of Information Transmission, 1998, 34:4, 342–353

Bibliographic databases:

UDC: 621.391.1:681.327
Received: 06.03.1998
Revised: 05.06.1998

Citation: E. A. Karatsuba, “Fast Evaluation of the Hurwitz Zeta Function and Dirichlet $L$-Series”, Probl. Peredachi Inf., 34:4 (1998), 62–75

Citation in format AMSBIB
\Bibitem{Kar98}
\by E.~A.~Karatsuba
\paper Fast Evaluation of the Hurwitz Zeta Function and Dirichlet $L$-Series
\jour Probl. Peredachi Inf.
\yr 1998
\vol 34
\issue 4
\pages 62--75
\mathnet{http://mi.mathnet.ru/ppi425}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1793495}
\zmath{https://zbmath.org/?q=an:0928.11056}
\transl
\jour Problems Inform. Transmission
\yr 1998
\vol 34
\issue 4
\pages 342--353


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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. 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  mathscinet  zmath  isi
    2. Vepstas, L, “An efficient algorithm for accelerating the convergence of oscillatory series, useful for computing the polylogarithm and Hurwitz zeta functions”, Numerical Algorithms, 47:3 (2008), 211  crossref  mathscinet  zmath  adsnasa  isi
    3. Lampret V., “An interplay between a generalized-Euler-constant function and the Hurwitz zeta function”, Bull Belg Math Soc Simon Stevin, 17:4 (2010), 741–747  mathscinet  zmath  isi
    4. С. В. Яхонтов, “Эффективное по времени и памяти вычисление логарифмической функции вещественного аргумента на машине Шëнхаге”, ПДМ, 2013, № 2(20), 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  mathscinet  elib; 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
    6. Е. А. Карацуба, “Об одном методе быстрого приближения дзета-констант рациональными дробями”, Пробл. передачи информ., 50:2 (2014), 77–95  mathnet; E. A. Karatsuba, “On one method for fast approximation of zeta constants by rational fractions”, Problems Inform. Transmission, 50:2 (2014), 186–202  crossref  isi  elib
    7. Е. А. Карацуба, “Об одном методе построения семейства аппроксимаций дзета-констант рациональными дробями”, Пробл. передачи информ., 51:4 (2015), 78–91  mathnet; 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  crossref  isi  elib
    8. Karatsuba E.A., “Fast Approximations of Certain Number-Theoretic Constants”, Dokl. Math., 91:3 (2015), 283–286  crossref  mathscinet  zmath  isi  elib
  • Проблемы передачи информации Problems of Information Transmission
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