Relations between exceptional sets for additive problems

被引：18

作者：

Kawada, Koichi ^{[1
]}

Wooley, Trevor D. ^{[2
]}

机构：

[1] Iwate Univ, Dept Math, Fac Educ, Morioka, Iwate 0208550, Japan

[2] Univ Bristol, Sch Math, Bristol BS8 1TW, Avon, England

来源：

JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES | 2010年 / 82卷

关键词：

WARINGS PROBLEM; HIGHER POWERS; SUMS; CUBES; IMPROVEMENTS; SQUARES; NUMBER;

D O I：

10.1112/jlms/jdq036

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We describe a method for bounding the set of exceptional integers not represented by a given additive form in terms of the exceptional set corresponding to a subform. Illustrating our ideas with examples stemming from Waring's problem for cubes, we show, in particular, that the number of positive integers not exceeding N that fail to have a representation as the sum of six cubes of natural numbers is O(N(3/7)).

引用

页码：437 / 458

页数：22

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