This article is cited 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

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.

UDC: 517.524+511.622+511.37

MSC: Primary 11N37; Secondary 11L05, 11K50, 11A55

Received: 27.03.2012 and 19.09.2012

DOI: 10.4213/sm8123

 English version: Sbornik: Mathematics, 2013, 204:5, 762–779

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