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A light-weight version of Waring's problem

Part of: Additive number theory; partitions

Published online by Cambridge University Press:  09 April 2009

Trevor D. Wooley
Trevor D. Wooley
Affiliation:
Department of Mathematics, University of Michigan, East Hall, 525 East University Ave, Ann Arbor, MI 48109-1109, USA e-mail: wooley@umich.edu
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Abstract

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An asymptotic formula is established for the number of representations of a large integer as the sum of kth powers of natural numbers, in which each representation is counted with a homogeneous weight that de-emphasises the large solutions. Such an asymptotic formula necessarily fails when this weight is excessively light.

Keywords

Waring's problemapplications of the Hardy-Littlewood method

MSC classification

Secondary: 11P05: Waring's problem and variants 11P55: Applications of the Hardy-Littlewood method

Information

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 76 , Issue 3 , June 2004 , pp. 303 - 316
Copyright
Copyright © Australian Mathematical Society 2004

References

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