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Problemy Peredachi Informatsii, 1998, Volume 34, Issue 4, Pages 62–75 (Mi ppi425)  
This article is cited in 10 scientific papers (total in 10 papers)

Automata Theory

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

E. A. Karatsuba
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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.
Received: 06.03.1998
Revised: 05.06.1998
Bibliographic databases:
UDC: 621.391.1:681.327
Language: Russian
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://mathscinet.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
Linking options:
  • https://www.mathnet.ru/eng/ppi425
  • https://www.mathnet.ru/eng/ppi/v34/i4/p62
    • 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
    9. E. A. Karatsuba, “On computation of the Bessel function by summing up the series”, Num. Anal. Appl., 12:4 (2019), 372–387  mathnet  crossref  crossref  isi
    10. Johansson F., “Computing Hypergeometric Functions Rigorously”, ACM Trans. Math. Softw., 45:3 (2019), 30  crossref  mathscinet  zmath  isi  scopus
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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