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Russian Mathematical Surveys, 2007, Volume 62, Issue 5, Pages 843–855
DOI: https://doi.org/10.1070/RM2007v062n05ABEH004453 (Mi rm8504) 		 
This article is cited in 13 scientific papers (total in 14 papers)

Continued fractions of square roots of rational numbers and their statistics

V. I. Arnol'd

Steklov Mathematical Institute, Russian Academy of Sciences
English version PDF (390 kB) Citations (14)
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DOI: https://doi.org/10.1070/RM2007v062n05ABEH004453
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.
Received: 14.03.2007
Russian version:
Uspekhi Matematicheskikh Nauk, 2007, Volume 62, Issue 5(377), Pages 3–14
DOI: https://doi.org/10.4213/rm8504
Bibliographic databases:
Document Type: Article
UDC: 511+517.938+519.22
MSC: Primary 11J70; Secondary 11A55, 11K50
Language: English
Original paper language: Russian
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
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    • This publication is cited in the following 14 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    References:125
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