Distribution of rational points on the circle of unit radius

M. A. Korolev^a, A. V. Ustinov<sup>b

a</sup> 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.

UDC: 511.321

MSC: Primary 14G05; Secondary 11B83, 11N60, 62E20, 97K60

Received: 05.07.2018

DOI: 10.4213/im8839

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

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