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Funktsional. Anal. i Prilozhen., 2004, Volume 38, Issue 2, Pages 1–11 (Mi faa103)  

This article is cited in 16 scientific papers (total in 16 papers)

On the Statistics of Partial Quotients of Finite Continued Fractions

M. O. Avdeevaab

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

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


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English version:
Functional Analysis and Its Applications, 2004, 38:2, 79–87

Bibliographic databases:

UDC: 511.36+511.37
Received: 06.02.2003

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
\by M.~O.~Avdeeva
\paper On the Statistics of Partial Quotients of Finite Continued Fractions
\jour Funktsional. Anal. i Prilozhen.
\yr 2004
\vol 38
\issue 2
\pages 1--11
\jour Funct. Anal. Appl.
\yr 2004
\vol 38
\issue 2
\pages 79--87

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    This publication is cited in the following articles:
    1. A. V. Ustinov, “On the statistical properties of finite continued fractions”, J. Math. Sci. (N. Y.), 137:2 (2006), 4722–4738  mathnet  crossref  mathscinet  zmath
    2. V. A. Bykovskii, “Estimate for dispersion of lengths of continued fractions”, J. Math. Sci., 146:2 (2007), 5634–5643  mathnet  crossref  mathscinet  zmath
    3. A. V. Ustinov, “On Gauss–Kuz'min statistics for finite continued fractions”, J. Math. Sci., 146:2 (2007), 5771–5781  mathnet  crossref  mathscinet  zmath
    4. V. I. Arnol'd, “Continued fractions of square roots of rational numbers and their statistics”, Russian Math. Surveys, 62:5 (2007), 843–855  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    5. A. V. Ustinov, “Calculation of the variance in a problem in the theory of continued fractions”, Sb. Math., 198:6 (2007), 887–907  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    6. O. N. Karpenkov, “On an Invariant Möbius Measure and the Gauss–Kuzmin Face Distribution”, Proc. Steklov Inst. Math., 258 (2007), 74–86  mathnet  crossref  mathscinet  zmath  elib  elib
    7. 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  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    8. V. I. Arnol'd, “Statistics of the periods of continued fractions for quadratic irrationals”, Izv. Math., 72:1 (2008), 1–34  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    9. 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  mathnet  crossref  crossref  mathscinet  zmath  isi
    10. 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  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    11. O. N. Karpenkov, “Determination of Periods of Geometric Continued Fractions for Two-Dimensional Algebraic Hyperbolic Operators”, Math. Notes, 88:1 (2010), 28–38  mathnet  crossref  crossref  mathscinet  isi
    12. A. V. Ustinov, “The Mean Number of Steps in the Euclidean Algorithm with Odd Incomplete Quotients”, Math. Notes, 88:4 (2010), 574–584  mathnet  crossref  crossref  mathscinet  isi
    13. 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  crossref  mathscinet  zmath  isi  elib  scopus
    14. Shparlinski I.E., “Modular Hyperbolas”, Jap. J. Math., 7:2 (2012), 235–294  crossref  mathscinet  zmath  isi  elib  scopus
    15. 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  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    16. A. V. Ustinov, “Three-dimensional continued fractions and Kloosterman sums”, Russian Math. Surveys, 70:3 (2015), 483–556  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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