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Izvestiya: Mathematics, 2019, Volume 83, Issue 5, Pages 1008–1049
DOI: https://doi.org/10.1070/IM8839 (Mi im8839) 		 
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
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DOI: https://doi.org/10.1070/IM8839
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).
Received: 05.07.2018
Russian version:
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya, 2019, Volume 83, Issue 5, Pages 107–148
DOI: https://doi.org/10.4213/im8839
Bibliographic databases:
Document Type: Article
UDC: 511.321
MSC: Primary 14G05; Secondary 11B83, 11N60, 62E20, 97K60
Language: English
Original paper language: Russian
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
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