|
This article is cited in 9 scientific papers (total in 9 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.
 Full text:
PDF file (991 kB)
References:
PDF file
HTML file
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
Linking options:
http://mi.mathnet.ru/eng/ppi425 http://mi.mathnet.ru/eng/ppi/v34/i4/p62
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:
-
Karatsuba E.A., “Fast computation of (3) and of some special integrals using the Ramanujan formula and polylogarithms”, BIT, 41:4 (2001), 722–730
  -
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
 -
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
-
S. V. Yakhontov, “Effektivnoe po vremeni i pamyati vychislenie logarifmicheskoi funktsii veschestvennogo argumenta na mashine Shenkhage”, PDM, 2013, no. 2(20), 101–114
 -
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
 -
E. A. Karatsuba, “On one method for fast approximation of zeta constants by rational fractions”, Problems Inform. Transmission, 50:2 (2014), 186–202
-
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
-
Karatsuba E.A., “Fast Approximations of Certain Number-Theoretic Constants”, Dokl. Math., 91:3 (2015), 283–286
-
E. A. Karatsuba, “O vychislenii funktsii Besselya putem summirovaniya ryadov”, Sib. zhurn. vychisl. matem., 22:4 (2019), 453–472
|
| Number of views: |
| This page: | 573 | | Full text: | 153 | | References: | 35 |
|
Terms of Use