The Distribution of Rational Points on the Unit Circle

Affiliation:
Pacific National University
Khabarovsk Division of the Institute for Applied Mathematics, Far Eastern Branch, Russian Academy of Sciences

M. Korolev

Affiliation: Steklov mathematical institute of Russian Academy of sciences

Journal name

Doklady Akademii nauk

Edition

Volume 481 Issue 2

Pages

131-135

Abstract

In the paper, the explicit form of distribution function for the lengths of arcs connecting neighbouring rational points on the unit circle whose denominators do not exceed given value, is given.

Keywords

rational points, unit circle, Farey fractions, distribution function

Received

05.10.2018

Publication date

14.10.2018

Number of characters

152

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GOST	Ustinov A., Korolev M. The Distribution of Rational Points on the Unit Circle // Doklady Akademii nauk – 2018. – V. 481. – Issue 2 C. 131-135 [Electronic resource]. URL: http://ras.jes.su/dan/s207987840000225-6-2-en (circulation date: 08.05.2024). DOI: 10.31857/S086956520001188-9
MLA	Ustinov, A., Korolev, M. "The Distribution of Rational Points on the Unit Circle." Doklady Akademii nauk 481.2 (2018):131-135. DOI: 10.31857/S086956520001188-9
APA	Ustinov A., Korolev M. (2018). The Distribution of Rational Points on the Unit Circle. Doklady Akademii nauk 481(2), pp.131-135 DOI: 10.31857/S086956520001188-9

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1. Ustinov A.V. O chisle reshenij sravneniya xy ≡ l(mod q) pod grafikom dvazhdy nepreryvno differentsiruemoj funktsii // Algebra i analiz. 2008. T. 20. № 5. S. 186–216.

2. Boca F.P., Cobeli C., Zaharescu A. Distribution of lattice Points Visible from the Origin // Commun. Math. Phys. 2000. V. 213. P. 433–470.