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On the index of fractions with square-free denominators in arithmetic progressions |
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| Authors: | Emre Alkan Andrew H. Ledoan Marian Vâjâitu Alexandru Zaharescu |
| Affiliation: | (1) Department of Mathematics, University of Illinois at Urbana-Champaign, 273 Altgeld Hall, MC-382, 1409 W. Green Street, Urbana, IL 61801-2975, USA;(2) “Simion Stoilow” Institute of Mathematics, Romanian Academy, P.O. Box 1-764, Bucharest, 014700, Romania |
| 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→∞. 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. |
| Keywords: | Index of Farey fractions Square-free integers Riemann zeta-function and Dirichlet L-functions Arithmetic progressions |
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