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DAVENPORT’S METHOD AND SLIM EXCEPTIONAL SETS: THE ASYMPTOTIC FORMULAE IN WARING’S PROBLEM

Published online by Cambridge University Press:  13 July 2010

Koichi Kawada
Affiliation:
Department of Mathematics, Faculty of Education, Iwate University, Morioka 020-8550, Japan (email: [email protected])
Trevor D. Wooley
Affiliation:
School of Mathematics, University of Bristol, University Walk, Clifton, Bristol BS8 1TW, U.K. (email: [email protected])
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Abstract

We apply a method of Davenport to improve several estimates for slim exceptional sets associated with the asymptotic formula in Waring’s problem. In particular, we show that the anticipated asymptotic formula in Waring’s problem for sums of seven cubes holds for all but O(N1/3+ε) of the natural numbers not exceeding N.

Type
Research Article
Copyright
Copyright © University College London 2010

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