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

Koichi Kawada*, Trevor D. Wooley

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)

6 Citations (Scopus)

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+epsilon) of the natural numbers not exceeding N.

Original languageEnglish
Pages (from-to)305-321
Number of pages17
JournalMathematika
Volume56
Issue number2
DOIs
Publication statusPublished - Jul 2010

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