Continuous distributions arising from the Three Gap Theorem

DOI10.1142/S1793042116501074zbMath1396.11041arXiv1511.09399MaRDI QIDQ2828356

Daniel Schultz, Alexandru Zaharescu, Geremías Polanco

Publication date: 25 October 2016

Published in: International Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1511.09399

zbMATH Keywords

uniform distributionFarey fractionscontinuous distributionthree gap theorem

Mathematics Subject Classification ID

Well-distributed sequences and other variations (11K36) Farey sequences; the sequences (1^k, 2^k, dots) (11B57) Distribution modulo one (11J71)

Related Items (3)

Deviation from equidistance for one-dimensional sequences ⋮ Lochs-type theorems beyond positive entropy ⋮ Systems of rank one, explicit Rokhlin towers, and covering numbers

Cites Work

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• On small fractional parts of polynomials
• On integer and fractional parts of powers of Salem numbers
• The h-spacing distribution between Farey points
• The distribution of spacings between fractional parts of lacunary sequences
• On successive settings of an arc on the circumference of a circle
• On consecutive Farey arcs
• ON THE FRACTIONAL PARTS OF RATIONAL POWERS
• The application of a new mean value theorem to the fractional parts of polynomials
• On consecutive Farey arcs II
• The generic spacing distribution of the two-dimensional harmonic oscillator
• Generalization of a theorem of Steinhaus
• The distribution of spacings between the fractional parts of \(n^2\alpha\)

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