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A note on the pair correlation of Farey fractions

Volume 205 / 2022

Florin P. Boca, Maria Siskaki Acta Arithmetica 205 (2022), 121-135 MSC: Primary 11J71; Secondary 11B57, 11K38. DOI: 10.4064/aa210926-30-8 Published online: 22 September 2022

Abstract

The pair correlations of Farey fractions with denominators $q$ satisfying $(q,m)=1$, respectively $q\equiv b \bmod {m}$ with $(b,m)=1$, are shown to exist and are explicitly computed.

Authors

  • Florin P. BocaDepartment of Mathematics
    University of Illinois at Urbana-Champaign
    Urbana, IL 61801, USA
    e-mail
  • Maria SiskakiDepartment of Mathematics
    University of Illinois at Urbana-Champaign
    Urbana, IL 61801, USA
    e-mail

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