Spin chains and Arnold's problem on the Gauss-Kuz'min statistics for quadratic irrationals

DOI10.1070/SM2013v204n05ABEH004319zbMath1288.11092MaRDI QIDQ2848648

Alexey Ustinov

Publication date: 26 September 2013

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

Full work available at URL: http://iopscience.iop.org/1064-5616/page/Abstracted

zbMATH Keywords

Kloosterman sumcontinued fractionquadratic irrational

Mathematics Subject Classification ID

Estimates on exponential sums (11L07) Asymptotic results on arithmetic functions (11N37) Continued fractions (11A55) Metric theory of continued fractions (11K50)

Related Items (5)

Distribution of the periodic points of the Farey map ⋮ Distribution of periodic points of certain Gauss shifts with infinite invariant measure ⋮ Distribution of the reduced quadratic irrationals arising from the odd continued fraction expansion ⋮ Gaussian behavior of quadratic irrationals ⋮ On points of the modular hyperbola under the graph of a linear function

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• The mean number of steps in the Euclidean algorithm with odd partial quotients
• Statistik der Teilnenner der zu den echten Brüchen gehörigen regelmäßigen Kettenbrüche
• Estimate for dispersion of lengths of continued fractions
• On Gauss-Kuz'min statistics for finite continued fractions
• A Farey fraction spin chain
• The phase transition in statistical models defined on Farey fractions
• On the statistics of partial quotients of finite continued fractions
• On the distribution of Frobenius numbers with three arguments
• On the number of solutions of the congruence $xy\equiv l\pmod {q}$ under the graph of a twice continuously differentiable function
• On certain statistical properties of continued fractions with even and with odd partial quotients
• The statistics of particle trajectories in the inhomogeneous Sinai problem for a two-dimensional lattice
• Distribution of Lévy constants for quadratic numbers
• Products of matrices and and the distribution of reduced quadratic irrationals
• On Kloosterman's sum
• Class numbers of indefinite binary quadratic forms
• The limit distribution of a number theoretic function arising from a problem in statistical mechanics
• On asymptotic properties of a number theoretic function arising out of a spin chain model in statistical mechanics

This page was built for publication: Spin chains and Arnold's problem on the Gauss-Kuz'min statistics for quadratic irrationals