In this paper, we focus on the pair correlation of fractions whose denominators are products of primes. We show that the limiting pair correlation function of such fractions on any short interval ${\bf I}\subset [0,1]$ exists and is independent of ${\bf I}$ . Furthermore, we use this result to compute the pair correlation function of the angles of elements in specific types of regions.

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Volume298, Issue7

July 2025

Pages 2263-2281

Correlations of fractions whose denominators are products of primes

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Correlations of fractions whose denominators are products of primes

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