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A light-weight version of Waring's problem

Published online by Cambridge University Press:  09 April 2009

Trevor D. Wooley
Affiliation:
Department of Mathematics, University of Michigan, East Hall, 525 East University Ave, Ann Arbor, MI 48109-1109, USA e-mail: [email protected]
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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.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 2004

References

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