On the statistical properties of finite continued fractions

DOI10.1007/s10958-006-0268-6zbMath1072.11060OpenAlexW2072601494MaRDI QIDQ558754

Alexey Ustinov

Publication date: 14 July 2005

Published in: Journal of Mathematical Sciences (New York) (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/227267

zbMATH Keywords

continued fractionsmetric theory

Mathematics Subject Classification ID

Continued fractions (11A55) Metric theory of continued fractions (11K50)

Related Items (7)

Modular hyperbolas ⋮ Bias in the number of steps in the Euclidean algorithm and a conjecture of Ito on Dedekind sums ⋮ The law of large numbers for the sum of the partial quotients of a rational number with fixed denominator ⋮ The average length of finite continued fractions with fixed denominator ⋮ Estimate for dispersion of lengths of continued fractions ⋮ On Gauss-Kuz'min statistics for finite continued fractions ⋮ On the number of solutions of the congruence $xy\equiv l\pmod {q}$ under the graph of a twice continuously differentiable function

Cites Work

• Evaluation of Porter's constant
• Fermat dynamics, matrix arithmetics, finite circles, and finite Lobachevsky planes
• On a theorem of Heilbronn
• The number of steps in the Euclidean algorithm
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