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

Emre Alkan; Andrew H. Ledoan; Marian Vâjâitu; Alexandru Zaharescu

doi:10.1007/s11139-007-9103-z

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

Emre Alkan
, Andrew H. Ledoan
, Marian Vâjâitu
, Alexandru Zaharescu

Mathematics

Research output: Contribution to journal › Article › peer-review

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→∞.

Original language	English (US)
Pages (from-to)	131-161
Number of pages	31
Journal	Ramanujan Journal
Volume	16
Issue number	2
DOIs	https://doi.org/10.1007/s11139-007-9103-z
State	Published - Jul 2008

Keywords

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

ASJC Scopus subject areas

Algebra and Number Theory

Online availability

10.1007/s11139-007-9103-z

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title = "On the index of fractions with square-free denominators in arithmetic progressions",

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

author = "Emre Alkan and Ledoan, \{Andrew H.\} and Marian V{\^a}j{\^a}itu and Alexandru Zaharescu",

note = "A. Zaharescu was supported by NSF grant number DMS-0456615. This research was also partially supported by the CERES Program 4-147/2004 of the Romanian Ministry of Education and Research.",

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AU - Ledoan, Andrew H.

AU - Vâjâitu, Marian

AU - Zaharescu, Alexandru

N1 - A. Zaharescu was supported by NSF grant number DMS-0456615. This research was also partially supported by the CERES Program 4-147/2004 of the Romanian Ministry of Education and Research.

PY - 2008/7

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AB - 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→∞.

KW - Arithmetic progressions

KW - Index of Farey fractions

KW - Riemann zeta-function and Dirichlet L-functions

KW - Square-free integers

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

Abstract

Keywords

ASJC Scopus subject areas

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