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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.
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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http://mi.mathnet.ru/eng/izv8839https://doi.org/10.4213/im8839 http://mi.mathnet.ru/eng/izv/v83/i5/p107
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