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Izv. RAN. Ser. Mat., 2019, Volume 83, Issue 5, Pages 107–148 (Mi izv8839)  
Distribution of rational points on the circle of unit radius

M. A. Koroleva, A. V. Ustinovb

a Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
b Pacific National University, Khabarovsk

Abstract: We obtain an expression for the density of the distribution of the lengths of arcs connecting neighbouring rational points on the unit circle with denominators not exceeding a given bound.

Keywords: Farey fractions, Pythagorean triples, unit circle, density of a distribution.

Funding Agency Grant Number
Russian Academy of Sciences - Federal Agency for Scientific Organizations PRAS 18-01
Russian Science Foundation 18-41-05001
When writing this work, the first author was supported by the Programme of the Presidium of the Russian Academy of Sciences no. 01 “Fundamental Mathematics and its Applications” (grant PRAS 18-01). The research of the second author (§ 3) was funded by a grant from the Russian Science Foundation (project no. 18-41-05001).


DOI: https://doi.org/10.4213/im8839

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English version:
Izvestiya: Mathematics, 2019, 83:5, 1008–1049

UDC: 511.321
MSC: Primary 14G05; Secondary 11B83, 11N60, 62E20, 97K60
Received: 05.07.2018

Citation: M. A. Korolev, A. V. Ustinov, “Distribution of rational points on the circle of unit radius”, Izv. RAN. Ser. Mat., 83:5 (2019), 107–148; Izv. Math., 83:5 (2019), 1008–1049

Citation in format AMSBIB
\Bibitem{KorUst19}
\by M.~A.~Korolev, A.~V.~Ustinov
\paper Distribution of rational points on the circle of unit radius
\jour Izv. RAN. Ser. Mat.
\yr 2019
\vol 83
\issue 5
\pages 107--148
\mathnet{http://mi.mathnet.ru/izv8839}
\crossref{https://doi.org/10.4213/im8839}
\transl
\jour Izv. Math.
\yr 2019
\vol 83
\issue 5
\pages 1008--1049
\crossref{https://doi.org/10.1070/IM8839}


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