Article

The Ramanujan Journal

, Volume 16, Issue 2, pp 131-161

First online:

On the index of fractions with square-free denominators in arithmetic progressions

  • Emre AlkanAffiliated withDepartment of Mathematics, University of Illinois at Urbana-Champaign
  • , Andrew H. LedoanAffiliated withDepartment of Mathematics, University of Illinois at Urbana-Champaign
  • , Marian VâjâituAffiliated with“Simion Stoilow” Institute of Mathematics, Romanian Academy
  • , Alexandru ZaharescuAffiliated withDepartment of Mathematics, University of Illinois at Urbana-Champaign Email author 

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Abstract

We prove asymptotic formulas for the first and second moments of the index of fractions with square-free denominators of order Q streaming in a given arithmetic progression as Q→∞.

Keywords

Index of Farey fractions Square-free integers Riemann zeta-function and Dirichlet L-functions Arithmetic progressions

Mathematics Subject Classification (2000)

11B57 11M06 11N25