On Vinogradov's mean value theorem: strongly diagonal behaviour via efficient congruencing
成果类型：
Article
署名作者：
Ford, Kevin; Wooley, Trevor D.
署名单位：
University of Illinois System; University of Illinois Urbana-Champaign; University of Bristol
刊物名称：
ACTA MATHEMATICA
ISSN/ISSBN：
0001-5962
DOI：
10.1007/s11511-014-0119-0
发表日期：
2014
页码：
199-236
关键词：
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.
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