Sbornik: Mathematics
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS


Mat. Sb.:
Year:
Volume:
Issue:
Page:
Find




Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register

Sbornik: Mathematics, 2009, Volume 200, Issue 8, Pages 1181–1214
DOI: https://doi.org/10.1070/SM2009v200n08ABEH004034 (Mi sm6367) 		 
This article is cited in 6 scientific papers (total in 6 papers)

The average length of reduced regular continued fractions

E. N. Zhabitskaya

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
English version PDF (435 kB) Citations (6)
References:
PDF
HTML
DOI: https://doi.org/10.1070/SM2009v200n08ABEH004034
Abstract: Let $l(a/b)$ be the number of steps of the by-excess Euclidean algorithm applied to the numbers $a$ and $b$. In this paper we obtain a three-term asymptotic formula for the expectation of the random value $l(a/b)$, when $1\le a\le b\le R$ and $R\to\infty$.
Bibliography: 11 titles.
Keywords: Euclidean algorithm, division by-excess, average length, continued fraction.
Received: 21.05.2008 and 27.03.2009
Russian version:
Matematicheskii Sbornik, 2009, Volume 200, Number 8, Pages 79–110
DOI: https://doi.org/10.4213/sm6367
Bibliographic databases:
UDC: 511.335
MSC: Primary 11A55; Secondary 11K50
Language: English
Original paper language: Russian
Citation: E. N. Zhabitskaya, “The average length of reduced regular continued fractions”, Mat. Sb., 200:8 (2009), 79–110; Sb. Math., 200:8 (2009), 1181–1214
Citation in format AMSBIB
\Bibitem{Zha09}
\by E.~N.~Zhabitskaya
\paper The average length of reduced regular continued fractions
\jour Mat. Sb.
\yr 2009
\vol 200
\issue 8
\pages 79--110
\mathnet{http://mi.mathnet.ru/sm6367}
\crossref{https://doi.org/10.4213/sm6367}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2573013}
\zmath{https://zbmath.org/?q=an:05636172}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2009SbMat.200.1181Z}
\elib{https://elibrary.ru/item.asp?id=19066149}
\transl
\jour Sb. Math.
\yr 2009
\vol 200
\issue 8
\pages 1181--1214
\crossref{https://doi.org/10.1070/SM2009v200n08ABEH004034}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000271676400010}
\elib{https://elibrary.ru/item.asp?id=15477869}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-72849151737}
Linking options:
  • https://www.mathnet.ru/eng/sm6367
  • https://doi.org/10.1070/SM2009v200n08ABEH004034
  • https://www.mathnet.ru/eng/sm/v200/i8/p79
    • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Математический сборник Sbornik: Mathematics
    Statistics & downloads:
    Abstract page:446
    Russian version PDF:199
    English version PDF:6
    References:49
    First page:14
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024