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 Open image in new window . 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.

Keywords

Squarefree integers Arithmetic progressions Variance 

Mathematics Subject Classification

11N37 11N69 

Notes

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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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.EPFL SB MATHGEOM TAN MA C3 604 (Bâtiment MA)LausanneSwitzerland

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