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A note on the pair correlation of Farey fractions

Florin P. Boca,Maria Siskaki

ACTA ARITHMETICA（2022）

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Abstract
The pair correlations of Farey fractions with denominators $q$ satisfying $(q,m)=1$, respectively $q\equiv b \pmod{m}$ with $(b,m)=1$, are shown to exist and are explicitly computed.
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Key words
Farey fractions,pair correlation,Kloosterman sums
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