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A variance for k-free numbers in arithmetic progressions

Published online by Cambridge University Press:  19 October 2005

R. C. Vaughan
R. C. Vaughan
Affiliation:
Department of Mathematics, McAllister Building, Pennsylvania State University, University Park, PA 16802, USA. E-mail: rvaughan@math.psu.edu
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Abstract

The second moment for the the distribution of $k$-free numbers into arithmetic progression is studied and the asymptotic formula of Hooley-Montgomery type is obtained for a wider range of values for the modulus than hitherto. In the special case of squarefree numbers this improves on the theorem of Warlimont from 1980.

Keywords

11N25
Type
Research Article
Information
Proceedings of the London Mathematical Society , Volume 91 , Issue 3 , November 2005 , pp. 573 - 597
Copyright
2005 London Mathematical Society

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Footnotes

Research supported by NSA grant, no. MDA904-03-1-0082.