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

Koichi Kawada; Trevor D. Wooley

doi:10.1112/S0025579310001257

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 journal › Article (Academic Journal) › peer-review

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 language	English
Pages (from-to)	305-321
Number of pages	17
Journal	Mathematika
Volume	56
Issue number	2
DOIs	https://doi.org/10.1112/S0025579310001257
Publication status	Published - Jul 2010

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@article{a8be1a622ecd491eab39106c79ac97e1,

title = "DAVENPORT'S METHOD AND SLIM EXCEPTIONAL SETS: THE ASYMPTOTIC FORMULAE IN WARING'S PROBLEM",

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.",

author = "Koichi Kawada and Wooley, {Trevor D.}",

year = "2010",

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AU - Wooley, Trevor D.

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N2 - 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.

AB - 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.

U2 - 10.1112/S0025579310001257

DO - 10.1112/S0025579310001257

M3 - Article (Academic Journal)

SN - 0025-5793

VL - 56

SP - 305

EP - 321

JO - Mathematika

JF - Mathematika

IS - 2

ER -

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

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