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The distribution of r-tuples of square-free numbers

Published online by Cambridge University Press:  26 February 2010

Kai-Man Tsang
Kai-Man Tsang
Affiliation:
School of Mathematics, Institute for Advanced Study, Princeton, New Jersey 08540, U.S.A.
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Abstract

We use the Buchstab-Rosser sieve to derive an asymptotic formula for the distribution of those integers n for which the r numbers n + l1, n + l2,…, n + lr are all square-free. Our error estimate sharpens a similar result of Hall and is uniform in both r and maxl 1≤i≤r|li|.

Type
Research Article
Information
Mathematika , Volume 32 , Issue 2 , December 1985 , pp. 265 - 275
Copyright
Copyright © University College London 1985

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References

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