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On the distribution of squarefree integers in arithmetic progressions

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Abstract

We investigate the error term of the asymptotic formula for the number of squarefree integers up to some bound, and lying in some arithmetic progression . In particular, we prove an upper bound for its variance as a varies over \((\mathbb {Z}/q\mathbb {Z})^{\times }\) which considerably improves upon earlier work of Blomer.

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Acknowledgements

It is a great pleasure for the author to thank Philippe Michel and Ramon Moreira Nunes for interesting conversations related to the topics of this article. The financial support and the perfect working conditions provided by the École Polytechnique Fédérale de Lausanne are gratefully acknowledged.

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  1. EPFL SB MATHGEOM TAN MA C3 604 (Bâtiment MA), Station 8, 1015, Lausanne, Switzerland

    Pierre Le Boudec

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  1. Pierre Le Boudec
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Correspondence to Pierre Le Boudec.

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Le Boudec, P. On the distribution of squarefree integers in arithmetic progressions. Math. Z. 290, 421–429 (2018). https://doi.org/10.1007/s00209-017-2023-8

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  • DOI: https://doi.org/10.1007/s00209-017-2023-8

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