The average length of finite continued fractions with fixed denominator

DOI10.1070/SM8718zbMath1382.11048OpenAlexW2582021869MaRDI QIDQ5369344

V. A. Bykovskii, Dmitriy A. Frolenkov

Publication date: 17 October 2017

Published in: Sbornik: Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1070/sm8718

zbMATH Keywords

continued fractionsadditive divisor problemmetric theory of continued fractions

Mathematics Subject Classification ID

Metric theory of continued fractions (11K50)

Related Items (1)

Bias in the number of steps in the Euclidean algorithm and a conjecture of Ito on Dedekind sums

Uses Software

• DLMF

Cites Work

• Asymptotic formula for the convolution of a generalized divisor function
• On the statistical properties of finite continued fractions
• The mean number of steps in the Euclidean algorithm with odd partial quotients
• Statistik der Teilnenner der zu den echten Brüchen gehörigen regelmäßigen Kettenbrüche
• The mean number of steps in the Euclidean algorithm with least absolute value remainders
• Evaluation of Porter's constant
• On the number of solutions of the congruence $xy\equiv l\pmod {q}$ under the graph of a twice continuously differentiable function
• An Asymptotic Formula in the Theory of Numbers
• Bessel Functions of Purely Imaginary Order, with an Application to Second-Order Linear Differential Equations Having a Large Parameter
• On a theorem of Heilbronn
• The binary additive divisor problem
• Asymptotic formulae for the second moments of $ L$-series of holomorphic cusp forms on the critical line
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