On the index of fractions with square-free denominators in arithmetic progressions
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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→∞.
KeywordsIndex of Farey fractions Square-free integers Riemann zeta-function and Dirichlet L-functions Arithmetic progressions
Mathematics Subject Classification (2000)11B57 11M06 11N25
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