ON WARING'S PROBLEM: THREE CUBES AND A MINICUBE

被引：4

作者：

Bruedern, Joerg ^{[1
]}

Wooley, Trevor D. ^{[2
]}

机构：

[1] Math Inst, D-37073 Gottingen, Germany

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

来源：

NAGOYA MATHEMATICAL JOURNAL | 2010年 / 200卷

关键词：

SUMS;

D O I：

10.1215/00277630-2010-012

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We establish that almost all natural numbers n are the sum of four cubes of positive integers, one of which is no larger than n(5/36). The proof makes use of an estimate for a certain eighth moment of cubic exponential sums, restricted to minor arcs only, of independent interest.

引用

页码：59 / 91

页数：33

共 18 条

[1] A REDUCTION TECHNIQUE IN WARINGS PROBLEM .1.
BOKLAN, KD
[J]. ACTA ARITHMETICA, 1993, 65 (02) : 147 - 161
[2] SUMS OF 4 CUBES
BRUDERN, J
[J]. MONATSHEFTE FUR MATHEMATIK, 1989, 107 (03): : 179 - 188
[3] On Waring's problem:: Three cubes and a sixth power
Brüdern, J
Wooley, TD
[J]. NAGOYA MATHEMATICAL JOURNAL, 2001, 163 : 13 - 53
[4] ON WARINGS PROBLEM FOR CUBES
BRUDERN, J
[J]. MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 1991, 109 : 229 - 256
[5] A PROBLEM IN ADDITIVE NUMBER-THEORY
BRUDERN, J
[J]. MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 1988, 103 : 27 - 33
[6] On Waring's problem for cubes
Davenport, H
[J]. ACTA MATHEMATICA, 1939, 71 (01) : 123 - 143
[7] DAVENPORT H., 2005, Analytic methods for Diophantine equations and Diophantine inequalities
[8] Hunt R.A., 1968, PROC C, P235
[9] On the sum of four cubes
Kawada, K
[J]. MATHEMATIKA, 1996, 43 (86) : 323 - 348
[10] Vaughan R. C., 1997, HARDY LITTLEWOOD MET

← 1 2 →