The cubic case of the main conjecture in Vinogradov's mean value theorem

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• 作者：Trevor D. Wooley ^{matdw@bristol.ac.uk" class="auth_mail" title="E-mail the corresponding author}
• 关键词：11L15 ; 11L07 ; 11P55
• 刊名：Advances in Mathematics
• 出版年：2016
• 出版时间：14 May 2016
• 年：2016
• 卷：294
• 期：Complete
• 页码：532-561
• 全文大小：502 K

文摘

We apply a variant of the multigrade efficient congruencing method to estimate Vinogradov's integral of degree 3 for moments of order 2s  , establishing strongly diagonal behaviour for 1⩽s⩽6$1⩽s⩽6$. Consequently, the main conjecture is now known to hold for the first time in a case of degree exceeding 2.