Products of matrices and and the distribution of reduced quadratic irrationals

DOI10.1515/CRELLE.2007.038zbMath1135.11050arXivmath/0503186MaRDI QIDQ5421663

Florin P. Boca

Publication date: 24 October 2007

Published in: Journal für die reine und angewandte Mathematik (Crelles Journal) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0503186

zbMATH Keywords

matricesDirichlet seriesquadratic irrationalsarithmetic functions

Mathematics Subject Classification ID

Asymptotic results on arithmetic functions (11N37) Other Dirichlet series and zeta functions (11M41) Matrices, determinants in number theory (11C20)

Related Items

Farey boat: continued fractions and triangulations, modular group and polygon dissections ⋮ Remark on the Farey fraction spin chain ⋮ Bias in the number of steps in the Euclidean algorithm and a conjecture of Ito on Dedekind sums ⋮ Distribution of the periodic points of the Farey map ⋮ Positive limit-Fourier transform of Farey fractions ⋮ Asymptotics of the Farey fraction spin chain free energy at the critical point ⋮ A thermodynamic classification of real numbers ⋮ -DEFORMED RATIONALS AND -CONTINUED FRACTIONS ⋮ Distribution of periodic points of certain Gauss shifts with infinite invariant measure ⋮ Spin chains and Arnold's problem on the Gauss-Kuz'min statistics for quadratic irrationals ⋮ Distribution of the reduced quadratic irrationals arising from the odd continued fraction expansion ⋮ Gaussian behavior of quadratic irrationals

Cites Work

• The index of a Farey sequence.
• Distribution of lattice points visible from the origin
• A Farey fraction spin chain
• The phase transition in statistical models defined on Farey fractions
• A fully magnetizing phase transition
• On asymptotic properties of a number theoretic function arising out of a spin chain model in statistical mechanics