The Ramanujan Journal

, Volume 16, Issue 2, pp 131–161

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

  • Emre Alkan
  • Andrew H. Ledoan
  • Marian Vâjâitu
  • Alexandru Zaharescu
Article

DOI: 10.1007/s11139-007-9103-z

Cite this article as:
Alkan, E., Ledoan, A.H., Vâjâitu, M. et al. Ramanujan J (2008) 16: 131. doi:10.1007/s11139-007-9103-z
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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 fractionsSquare-free integersRiemann zeta-function and Dirichlet L-functionsArithmetic progressions

Mathematics Subject Classification (2000)

11B5711M0611N25

Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  • Emre Alkan
    • 1
  • Andrew H. Ledoan
    • 1
  • Marian Vâjâitu
    • 2
  • Alexandru Zaharescu
    • 1
  1. 1.Department of MathematicsUniversity of Illinois at Urbana-ChampaignUrbanaUSA
  2. 2.“Simion Stoilow” Institute of MathematicsRomanian AcademyBucharestRomania