Journal of Mathematical Sciences

, Volume 137, Issue 2, pp 4722–4738

On statistical properties of finite continued fractions

  • A. V. Ustinov
Article

DOI: 10.1007/s10958-006-0268-6

Cite this article as:
Ustinov, A.V. J Math Sci (2006) 137: 4722. doi:10.1007/s10958-006-0268-6

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.

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