Vinogradov's mean value theorem via efficient congruencing, II

Trevor D. Wooley*

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

50 Citations (Scopus)


We apply the efficient congruencing method to estimate Vinogradov's integral for moments of order 2s, with 1 = k(2) - 1. In this way we come halfway to proving the main conjecture in two different directions. There are consequences for estimates of Weyl type and in several allied applications. Thus, for example, the anticipated asymptotic formula in Waring's problem is established for sums of s kth powers of natural numbers whenever s >= 2k(2) - 2k - 8 (k >= 6).

Original languageEnglish
Pages (from-to)673-730
Number of pages58
JournalDuke Mathematical Journal
Issue number4
Publication statusPublished - 15 Mar 2013


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