Distribution of rational points on the circle of unit radius

DOI10.1070/IM8839zbMath1436.11012OpenAlexW2982481764MaRDI QIDQ5241545

Alexey Ustinov, M. A. Korolev

Publication date: 31 October 2019

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

Full work available at URL: https://doi.org/10.1070/im8839

zbMATH Keywords

Pythagorean triplesunit circleFarey fractionsdensity of a distribution

Mathematics Subject Classification ID

Asymptotic distribution theory in statistics (62E20) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20) Dynamical systems in other branches of physics (quantum mechanics, general relativity, laser physics) (37N20) Congruences in many variables (11D79) Continued fractions (11A55) Special sequences and polynomials (11B83) Distribution functions associated with additive and positive multiplicative functions (11N60) Distributions and stochastic processes (educational aspects) (97K60) Dynamical systems with singularities (billiards, etc.) (37C83)

Cites Work

• The statistics of particle trajectories in the homogeneous Sinai problem for a two-dimensional lattice
• The statistics of the trajectory of a certain billiard in a flat two-torus
• Distribution of lattice points visible from the origin
• On the number of solutions of the congruence $xy\equiv l\pmod {q}$ under the graph of a twice continuously differentiable function
• The statistics of particle trajectories in the inhomogeneous Sinai problem for a two-dimensional lattice
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