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This article is cited in 11 scientific papers (total in 11 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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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
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\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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http://mi.mathnet.ru/eng/ppi425 http://mi.mathnet.ru/eng/ppi/v34/i4/p62
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This publication is cited in the following articles:
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Karatsuba E.A., “Fast computation of (3) and of some special integrals using the Ramanujan formula and polylogarithms”, BIT, 41:4 (2001), 722–730
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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
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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
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S. V. Yakhontov, “Effektivnoe po vremeni i pamyati vychislenie logarifmicheskoi funktsii veschestvennogo argumenta na mashine Shenkhage”, PDM, 2013, no. 2(20), 101–114
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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
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E. A. Karatsuba, “On one method for fast approximation of zeta constants by rational fractions”, Problems Inform. Transmission, 50:2 (2014), 186–202
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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
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Karatsuba E.A., “Fast Approximations of Certain Number-Theoretic Constants”, Dokl. Math., 91:3 (2015), 283–286
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E. A. Karatsuba, “O vychislenii funktsii Besselya putem summirovaniya ryadov”, Sib. zhurn. vychisl. matem., 22:4 (2019), 453–472
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Karatsuba E.A., “Calculation of Bessel Functions Via the Summation of Series”, Numer. Anal. Appl., 12:4 (2019), 372–387
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Johansson F., “Computing Hypergeometric Functions Rigorously”, ACM Trans. Math. Softw., 45:3 (2019), 30
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