RATIONAL POINTS ON LINEAR SLICES OF DIAGONAL HYPERSURFACES

被引：14

作者：

Bruedern, Joerg ^{[1
]}

Robert, Olivier ^{[2
,3
]}

机构：

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

[2] Univ Lyon, F-42000 St Etienne, France

[3] Univ St Etienne, Inst Camille Jordan, CNRS UMR 5208, F-42000 St Etienne, France

来源：

NAGOYA MATHEMATICAL JOURNAL | 2015年 / 218卷

关键词：

NONARY CUBIC FORMS; SIMULTANEOUS ADDITIVE EQUATIONS; MEAN-VALUE THEOREM; 2 HTH POWERS; WARING PROBLEM; SIEVE METHOD; NUMBERS; SUMS;

D O I：

10.1215/00277630-2891245

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

An asymptotic formula is obtained for the number of rational points of bounded height on the class of varieties described in the title line. The formula is proved via the Hardy-Littlewood method, and along the way we establish two new results on Weyl sums that are of some independent interest.

引用

页码：51 / 100

页数：50

共 37 条

[1]

[Anonymous], 2009, Analytic number theory. Essays in honour of K. F. Roth

[2] FORMS IN MANY VARIABLES [J].