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

Part of: Additive number theory; partitions

Published online by Cambridge University Press:  13 July 2010

Koichi Kawada  and
Trevor D. Wooley
Koichi Kawada
Affiliation:
Department of Mathematics, Faculty of Education, Iwate University, Morioka 020-8550, Japan (email: kawada@iwate-u.ac.jp)
Trevor D. Wooley
Affiliation:
School of Mathematics, University of Bristol, University Walk, Clifton, Bristol BS8 1TW, U.K. (email: matdw@bristol.ac.uk)
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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.

MSC classification

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

Information

Type
Research Article
Information
Mathematika , Volume 56 , Issue 2 , July 2010 , pp. 305 - 321
Copyright
Copyright © University College London 2010

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