Near-Optimal Mean Value Estimates for Multidimensional Weyl Sums

被引：24
作者：
Parsell, Scott T. [1 ]
Prendiville, Sean M. [2 ]
Wooley, Trevor D. [2 ]
机构：
[1] W Chester Univ, Dept Math, W Chester, PA 19383 USA
[2] Univ Bristol, Sch Math, Bristol BS8 1TW, Avon, England
来源：
GEOMETRIC AND FUNCTIONAL ANALYSIS | 2013年 / 23卷 / 06期
基金：
英国工程与自然科学研究理事会;
关键词：
VALUE THEOREM; POINTS;
D O I：
10.1007/s00039-013-0242-7
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We obtain sharp estimates for multidimensional generalisations of Vinogradov's mean value theorem for arbitrary translation-dilation invariant systems, achieving constraints on the number of variables approaching those conjectured to be the best possible. Several applications of our bounds are discussed.
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收藏
页码：1962 / 2024
页数：63
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