Vinogradov's mean value theorem via efficient congruencing

• 成果类型: Article
• 署名作者: Wooley, Trevor D.
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2012.175.3.12
• 发表日期: 2012
• 页码: 1575-1627
• 关键词: waring problem; weyl sums; cubes

摘要

We obtain estimates for Vinogradov's integral that for the first time approach those conjectured to be the best possible. Several applications of these new bounds are provided. In particular, the conjectured asymptotic formula in Waring's problem holds for sums of 8 kth powers of natural numbers whenever s >= 2k(2) + 2k - 3.