Correlations of Farey fractions with square-free denominators
Volume 220 / 2025
Acta Arithmetica 220 (2025), 323-344
MSC: Primary 11B57; Secondary 11J71, 11K06
DOI: 10.4064/aa240524-19-6
Published online: 30 September 2025
Abstract
This paper concerns the pair correlation of Farey fractions within an interval ${\bf I}\subset [0,1]$, specifically focusing on the fractions whose denominators are square-free numbers in an arithmetic sequence. We prove that the limiting pair correlation function of the sequence of such Farey fractions exists and is independent of the interval ${\bf I}$.
