On Vinogradov's mean value theorem: strongly diagonal behaviour via efficient congruencing

被引：15

作者：

Ford, Kevin ^{[1
]}

Wooley, Trevor D. ^{[2
]}

机构：

[1] Univ Illinois, Dept Math, Urbana, IL 61801 USA

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

来源：

ACTA MATHEMATICA | 2014年 / 213卷 / 02期

基金：

美国国家科学基金会;

关键词：

D O I：

10.1007/s11511-014-0119-0

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We enhance the efficient congruencing method for estimating Vinogradov's integral for moments of order 2s, with . In this way, we prove the main conjecture for such even moments when , showing that the moments exhibit strongly diagonal behaviour in this range. There are improvements also for larger values of s, these finding application to the asymptotic formula in Waring's problem.

引用

页码：199 / 236

页数：38

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