Matematicheskie Zametki
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. Zametki:
Year:
Volume:
Issue:
Page:
Find




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

Matematicheskie Zametki, 2010, Volume 88, Issue 4, Pages 594–604
DOI: https://doi.org/10.4213/mzm8854 (Mi mzm8854) 		 
This article is cited in 8 scientific papers (total in 8 papers)

The Mean Number of Steps in the Euclidean Algorithm with Odd Incomplete Quotients

A. V. Ustinov

Institute for Applied Mathematics, Khabarovsk Division, Far-Eastern Branch of the Russian Academy of Sciences
Full-text PDF (494 kB) Citations (8)
References:
PDF
HTML
DOI: https://doi.org/10.4213/mzm8854
Abstract: The length of the continued-fraction expansion of a rational number with odd incomplete quotients is expressed via the Gauss–Kuzmin statistics for the classical continued fraction. This has made it possible to prove asymptotic formulas, similar to those already known for the classical Euclidean algorithm, for the mean length of the Euclidean algorithm with odd incomplete quotients.
Keywords: Euclidean algorithm, Gauss–Kuzmin statistics, continued-fraction expansion, dual fraction, incomplete quotient.
Received: 13.04.2010
English version:
Mathematical Notes, 2010, Volume 88, Issue 4, Pages 574–584
DOI: https://doi.org/10.1134/S0001434610090300
Bibliographic databases:
Document Type: Article
UDC: 517.524+510.52+519.712.61
Language: Russian
Citation: A. V. Ustinov, “The Mean Number of Steps in the Euclidean Algorithm with Odd Incomplete Quotients”, Mat. Zametki, 88:4 (2010), 594–604; Math. Notes, 88:4 (2010), 574–584
Citation in format AMSBIB
\Bibitem{Ust10}
\by A.~V.~Ustinov
\paper The Mean Number of Steps in the Euclidean Algorithm with Odd Incomplete Quotients
\jour Mat. Zametki
\yr 2010
\vol 88
\issue 4
\pages 594--604
\mathnet{http://mi.mathnet.ru/mzm8854}
\crossref{https://doi.org/10.4213/mzm8854}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2882221}
\transl
\jour Math. Notes
\yr 2010
\vol 88
\issue 4
\pages 574--584
\crossref{https://doi.org/10.1134/S0001434610090300}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000284073100030}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-78249273608}
Linking options:
  • https://www.mathnet.ru/eng/mzm8854
  • https://doi.org/10.4213/mzm8854
  • https://www.mathnet.ru/eng/mzm/v88/i4/p594
    • This publication is cited in the following 8 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Математические заметки Mathematical Notes
    Statistics & downloads:
    Abstract page:620
    Full-text PDF :212
    References:58
    First page:16
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024