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Sbornik: Mathematics, 2013, Volume 204, Issue 5, Pages 762–779
DOI: https://doi.org/10.1070/SM2013v204n05ABEH004319 (Mi sm8123) 		 
This article is cited in 7 scientific papers (total in 7 papers)

Spin chains and Arnold's problem on the Gauss-Kuz'min statistics for quadratic irrationals

A. V. Ustinov

Institute for Applied Mathematics, Khabarovsk Division, Far-Eastern Branch of the Russian Academy of Sciences
English version PDF (372 kB) Citations (7)
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DOI: https://doi.org/10.1070/SM2013v204n05ABEH004319
Abstract: New results related to number theoretic model of spin chains are proved. We solve Arnold's problem on the Gauss-Kuz'min statistics for quadratic irrationals.
Bibliography: 24 titles.
Keywords: continued fractions, Kloosterman sums, quadratic irrationals.
Funding agency Grant number
Russian Foundation for Basic Research 11-01-12004-офи-м
Dynasty Foundation
Received: 27.03.2012 and 19.09.2012
Russian version:
Matematicheskii Sbornik, 2013, Volume 204, Number 5, Pages 143–160
DOI: https://doi.org/10.4213/sm8123
Bibliographic databases:
Document Type: Article
UDC: 517.524+511.622+511.37
MSC: Primary 11N37; Secondary 11L05, 11K50, 11A55
Language: English
Original paper language: Russian
Citation: A. V. Ustinov, “Spin chains and Arnold's problem on the Gauss-Kuz'min statistics for quadratic irrationals”, Mat. Sb., 204:5 (2013), 143–160; Sb. Math., 204:5 (2013), 762–779
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/sm/v204/i5/p143
    • This publication is cited in the following 7 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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