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

Trevor D Wooley

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

41 Citations (Scopus)
327 Downloads (Pure)

Abstract

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. Consequently, the main conjecture is now known to hold for the first time in a case of degree exceeding 2.
Original languageEnglish
Pages (from-to)532-561
Number of pages30
JournalAdvances in Mathematics
Volume294
Early online date21 Mar 2016
DOIs
Publication statusPublished - 14 May 2016

Keywords

  • math.NT
  • 11L15
  • 11L07
  • 11P55

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