On Vinogradov's mean value theorem: strongly diagonal behaviour via efficient congruencing

Kevin Ford, Trevor D. Wooley

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

16 Citations (Scopus)
281 Downloads (Pure)

Abstract

We enhance the efficient congruencing method for estimating Vinogradov’s integral for moments of order 2s, with 1⩽s⩽k2−1. In this way, we prove the main conjecture for such even moments when 1⩽s⩽14(k+1)2, 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.
Original languageEnglish
Pages (from-to)199-236
Number of pages38
JournalActa Mathematica
Volume213
Issue number2
Early online date25 Nov 2014
DOIs
Publication statusPublished - 1 Dec 2014

Keywords

  • math.NT
  • 11L15, 11L07, 11P05, 11P55

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