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Journal of Mathematical Sciences

, Volume 137, Issue 2, pp 4722–4738 | Cite as

On statistical properties of finite continued fractions

  • A. V. Ustinov
Article

Abstract

Statistical properties of continued fractions for numbers a/b, where a and b lie in the sector a, b ≥ 1, a2 + b2 ≤ R2, are studied. The main result is an asymptotic formula with two meaning terms for the quantity
$$N_x (R) = \sum\limits_{_{a,b \in \mathbb{N}}^{a^2 b^2 \leqslant R^2 } } {s_x (a/b)} ,$$
where sx(a/b) = ¦{j ε {1, …, s}: [0; tj, …, ts] ≤ x}¦ is the Gaussian statistic for the fraction a/b = [t0; t1, …, ts]. Bibliography: 12 titles.

Keywords

Asymptotic Formula Integral Point Continue Fraction Gaussian Statistic Asymptotic Relation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  • A. V. Ustinov
    • 1
    • 2
  1. 1.Moscow Lomonosov State UniversityKhabarovsk
  2. 2.Department of the Institute of Applied Mathematicsthe Far East Department of the Russian Academy of SciencesRussia

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