M. O. Avdeeva, “On the Statistics of Partial Quotients of Finite Continued Fractions”, Funktsional. Anal. i Prilozhen., 38:2 (2004), 1–11; Funct. Anal. Appl., 38:2 (2004), 79

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Funktsional'nyi Analiz i ego Prilozheniya, 2004, Volume 38, Issue 2, Pages 1–11
DOI: https://doi.org/10.4213/faa103 (Mi faa103)

This article is cited in 17 scientific papers (total in 17 papers)

On the Statistics of Partial Quotients of Finite Continued Fractions

M. O. Avdeeva^ab

^a Khabarovsk State Pedagogical University
^b Institute for Applied Mathematics, Khabarovsk Division, Far-Eastern Branch of the Russian Academy of Sciences

Full-text PDF (167 kB) Citations (17)

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DOI: https://doi.org/10.4213/faa103

Abstract: We refine the remainder estimate in the asymptotic formula, earlier obtained in a joint paper with V. A. Bykovskii, for Arnold's problem about Gauss–Kuzmin statistics.

Keywords: continued fraction, partial quotient, convergent, Gauss–Kuzmin statistics.

Received: 06.02.2003

English version:
Functional Analysis and Its Applications, 2004, Volume 38, Issue 2, Pages 79–87
DOI: https://doi.org/10.1023/B:FAIA.0000034038.55276.7d

Bibliographic databases:

Document Type: Article

UDC: 511.36+511.37

Language: Russian

Citation: M. O. Avdeeva, “On the Statistics of Partial Quotients of Finite Continued Fractions”, Funktsional. Anal. i Prilozhen., 38:2 (2004), 1–11; Funct. Anal. Appl., 38:2 (2004), 79–87

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/faa103

https://doi.org/10.4213/faa103

https://www.mathnet.ru/eng/faa/v38/i2/p1

This publication is cited in the following 17 articles:

A. V. Ustinov, “Three-dimensional continued fractions and Kloosterman sums”, Russian Math. Surveys, 70:3 (2015), 483–556
A. V. Ustinov, “Spin chains and Arnold's problem on the Gauss-Kuz'min statistics for quadratic irrationals”, Sb. Math., 204:5 (2013), 762–779
Shparlinski I.E., “Modular Hyperbolas”, Jap. J. Math., 7:2 (2012), 235–294
O. N. Karpenkov, “Determination of Periods of Geometric Continued Fractions for Two-Dimensional Algebraic Hyperbolic Operators”, Math. Notes, 88:1 (2010), 28–38
A. V. Ustinov, “The Mean Number of Steps in the Euclidean Algorithm with Odd Incomplete Quotients”, Math. Notes, 88:4 (2010), 574–584
Karpenkov O.N., Vershik A.M., “Rational approximation of maximal commutative subgroups of GL(n, R)”, J Fixed Point Theory Appl, 7:1 (2010), 241–263
V. A. Bykovskii, A. V. Ustinov, “The statistics of particle trajectories in the inhomogeneous Sinai problem for a two-dimensional lattice”, Izv. Math., 73:4 (2009), 669–688
A. V. Ustinov, “Asymptotic behaviour of the first and second moments for the number of steps in the Euclidean algorithm”, Izv. Math., 72:5 (2008), 1023–1059
V. I. Arnol'd, “Statistics of the periods of continued fractions for quadratic irrationals”, Izv. Math., 72:1 (2008), 1–34
V. A. Bykovskii, A. V. Ustinov, “The Statistics of Particle Trajectories in the Homogeneous Sinai Problem for a Two-Dimensional Lattice”, Funct. Anal. Appl., 42:3 (2008), 169–179
V. I. Arnol'd, “Continued fractions of square roots of rational numbers and their statistics”, Russian Math. Surveys, 62:5 (2007), 843–855
A. V. Ustinov, “Calculation of the variance in a problem in the theory of continued fractions”, Sb. Math., 198:6 (2007), 887–907
O. N. Karpenkov, “On an Invariant Möbius Measure and the Gauss–Kuzmin Face Distribution”, Proc. Steklov Inst. Math., 258 (2007), 74–86
Michael Trott, The Mathematica GuideBook for Numerics, 2006, 1
A. V. Ustinov, “On the statistical properties of finite continued fractions”, J. Math. Sci. (N. Y.), 137:2 (2006), 4722–4738
V. A. Bykovskii, “Estimate for dispersion of lengths of continued fractions”, J. Math. Sci., 146:2 (2007), 5634–5643
A. V. Ustinov, “On Gauss–Kuz'min statistics for finite continued fractions”, J. Math. Sci., 146:2 (2007), 5771–5781

Citing articles in Google Scholar: Russian citations, English citations
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