Analysis shows that pair correlation exists for Farey fractions with square-free denominators in intervals, indicating independence from the chosen interval.
This paper concerns the pair correlation of Farey fractions within an interval I⊂[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 I.
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Meijie Lu (2025) studied this question.
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