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The distribution of cube-full numbers

Published online by Cambridge University Press:  18 May 2009

P. Shiu
P. Shiu
Affiliation:
Department of Mathematical Sciences, Loughborough University, Loughborough, Leicestershire LE11 3TU, England
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Abstract

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An elementary derivation of the asymptotic formula for the number of cube-full numbers up to x is given. This derivation is used, together with an estimation of a three dimensional exponential sum, to establish the asymptotic formula for the number of cube-full numbers in the short interval x < n < x⅔+θ where 140/1123 < θ < 1/3.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 33 , Issue 3 , September 1991 , pp. 287 - 295
Copyright
Copyright © Glasgow Mathematical Journal Trust 1991

References

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