RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive
Impact factor
Subscription
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Uspekhi Mat. Nauk:
Year:
Volume:
Issue:
Page:
Find






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


Uspekhi Mat. Nauk, 2007, Volume 62, Issue 5(377), Pages 3–14 (Mi umn8504)  

This article is cited in 5 scientific papers (total in 6 papers)

Continued fractions of square roots of rational numbers and their statistics

V. I. Arnol'd

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: The differences are described between the statistics of the periodic continued fractions of quadratic irrational numbers and the universal Gauss–Kuzmin statistics of the continued fractions of random real numbers. Besides being a survey of these differences, this article discusses the results of V. A. Bykovskii [Bykovsky] and his school, who have proved the author's 1993 conjectures on the similarities of these statistics.

DOI: https://doi.org/10.4213/rm8504

Full text: PDF file (490 kB)
References: PDF file   HTML file

English version:
Russian Mathematical Surveys, 2007, 62:5, 843–855

Bibliographic databases:

UDC: 511+517.938+519.22
MSC: Primary 11J70; Secondary 11A55, 11K50
Received: 14.03.2007

Citation: V. I. Arnol'd, “Continued fractions of square roots of rational numbers and their statistics”, Uspekhi Mat. Nauk, 62:5(377) (2007), 3–14; Russian Math. Surveys, 62:5 (2007), 843–855

Citation in format AMSBIB
\Bibitem{Arn07}
\by V.~I.~Arnol'd
\paper Continued fractions of square roots of~rational numbers and their statistics
\jour Uspekhi Mat. Nauk
\yr 2007
\vol 62
\issue 5(377)
\pages 3--14
\mathnet{http://mi.mathnet.ru/umn8504}
\crossref{https://doi.org/10.4213/rm8504}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2373750}
\zmath{https://zbmath.org/?q=an:1147.11036}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?2007RuMaS..62..843A}
\elib{http://elibrary.ru/item.asp?id=25787448}
\transl
\jour Russian Math. Surveys
\yr 2007
\vol 62
\issue 5
\pages 843--855
\crossref{https://doi.org/10.1070/RM2007v062n05ABEH004453}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000253899500001}
\elib{http://elibrary.ru/item.asp?id=13534382}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-40749122583}


Linking options:
  • http://mi.mathnet.ru/eng/umn8504
  • https://doi.org/10.4213/rm8504
  • http://mi.mathnet.ru/eng/umn/v62/i5/p3

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    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:
    1. “Vladimir Igorevich Arnol'd (on his 70th birthday)”, Russian Math. Surveys, 62:5 (2007), 1021–1030  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    2. Aicardi F., “The sails of the $\mathrm{SL}(2,\mathbb Z)$ operators and their symmetries”, Funct. Anal. Other Math., 2:2-4 (2009), 93–110  crossref  mathscinet  zmath
    3. Aicardi F., “The continued fractions of the square roots of integers: on the parity of the length of their period”, Funct. Anal. Other Math., 3:1 (2010), 1–19  crossref  mathscinet  zmath
    4. Lerner E.Y., “About statistics of periods of continued fractions of quadratic irrationalities”, Funct. Anal. Other Math., 3:1 (2010), 75–83  crossref  mathscinet  zmath
    5. Aistleitner Ch., “on Some Questions of Vi Arnold on the Stochasticity of Geometric and Arithmetic Progressions”, 28, no. 10, 2015, 3663–3675  crossref  mathscinet  zmath  isi  scopus
    6. Aka M., Shapira U., “On the Evolution of Continued Fractions in a Fixed Quadratic Field”, J. Anal. Math., 134:1 (2018), 335–397  crossref  mathscinet  isi  scopus
  • Успехи математических наук Russian Mathematical Surveys
    Number of views:
    This page:1480
    Full text:417
    References:86
    First page:38

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020