The correlations of Farey fractions

2004/04/06 by Florin P. Boca, Alexandru Zaharescu, Boca, Florin P. +1 · 1 citation
Mathematics · #11B57 #11J71 #11K36 #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Limits and Structures in Graph Theory #Number Theory (math.NT) #math.NT #msc:11B57 #msc:11J71 #msc:11K36

paper · pdf · doi:10.48550/arxiv.math/0404114

18 pages, 1 figure. To appear in J. London Math. Soc

openalex publication_date 2004/04/06 · arxiv created 2005/01/19 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that all correlations of the sequence of Farey fractions exist and provide formulas for the correlation measures.

Citations

• Zeros of principal L-functions and random matrix theory

Cited by

• Farey neighbours, modular symbols and divergent geodesics

Related

• Pair correlation of Farey fractions with square-free denominators
• A note on the pair correlation of Farey fractions
• On the distribution of index of Farey Sequences
• On the distribution of polynomial Farey points and Chebyshev's bias phenomenon
• Distribution of Farey fractions with k-free denominators