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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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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; Problems Inform. Transmission, 34:4 (1998), 342–353

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. 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  mathscinet  zmath  isi  elib
  • Проблемы передачи информации Problems of Information Transmission
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