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Squarefree numbers on short intervals

Published online by Cambridge University Press:  26 February 2010

R. R. Hall
R. R. Hall
Affiliation:
Department of Mathematics, University of York, Heslington, York. YO1 5DD
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Extract

It is a familiar fact that the sequence of K-free numbers, i.e. those having no K-th power divisor greater than 1, has asymptotic density 1/ζ(K). Let χ(K) denote the characteristic function of this sequence, χ(2) = χ. Roth [5] proved that, if k/(n3/13(log n)4/13) → ∞, then

Type
Research Article
Information
Mathematika , Volume 29 , Issue 1 , June 1982 , pp. 7 - 17
Copyright
Copyright © University College London 1982

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References

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