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Probl. Peredachi Inf., 2015, Volume 51, Issue 4, Pages 78–91 (Mi ppi2189)  

This article is cited in 2 scientific papers (total in 2 papers)

Large Systems

On One method for constructing a family of approximations of zeta constants by rational fractions

E. A. Karatsuba

Dorodnitsyn Computing Center of the Federal Research Center "Computer Science and Control" of the Russian Academy of Sciences, Moscow, Russia

Abstract: We present a new method for fast approximation of zeta constants, i.e., values $\zeta(n)$ of the Riemann zeta function, $n\ge2$, $n$ is an integer, by rational fractions. The method makes it possible to fast approximate zeta constants and certain combinations of successive values of zeta constants by rational fractions. By choosing values of coefficients involved in the combinations, one can control the convergence rate of the approximations and the computation complexity for the zeta constants.

Funding Agency Grant Number
Russian Foundation for Basic Research 13-01-00657
Supported in part by the Russian Foundation for Basic Research, project no. 13-01-00657.


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English version:
Problems of Information Transmission, 2015, 51:4, 378–390

Bibliographic databases:

UDC: 621.391.1+517.521.15
Received: 21.07.2015
Revised: 07.09.2015

Citation: E. A. Karatsuba, “On One method for constructing a family of approximations of zeta constants by rational fractions”, Probl. Peredachi Inf., 51:4 (2015), 78–91; Problems Inform. Transmission, 51:4 (2015), 378–390

Citation in format AMSBIB
\Bibitem{Kar15}
\by E.~A.~Karatsuba
\paper On One method for constructing a~family of approximations of zeta constants by rational fractions
\jour Probl. Peredachi Inf.
\yr 2015
\vol 51
\issue 4
\pages 78--91
\mathnet{http://mi.mathnet.ru/ppi2189}
\elib{https://elibrary.ru/item.asp?id=26851366}
\transl
\jour Problems Inform. Transmission
\yr 2015
\vol 51
\issue 4
\pages 378--390
\crossref{https://doi.org/10.1134/S0032946015040079}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000367604200007}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84952940321}


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    Citing articles on Google Scholar: Russian citations, English citations
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    Erratum

    This publication is cited in the following articles:
    1. E. A. Karatsuba, “On an Identity with Binomial Coefficients”, Math. Notes, 105:1 (2019), 145–147  mathnet  crossref  crossref  mathscinet  isi  elib
    2. E. A. Karatsuba, “O metode vychisleniya dzeta-konstant, osnovannom na odnom teoretiko-chislovom podkhode”, Probl. peredachi inform., 57:3 (2021), 73–89  mathnet  crossref
  • Проблемы передачи информации Problems of Information Transmission
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