Approximating the main conjecture in Vinogradov's mean value theorem

Trevor D. Wooley

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

8 Citations (Scopus)
227 Downloads (Pure)

Abstract

We apply multigrade efficient congruencing to estimate Vinogradov's integral of degree k for moments of order 2s, establishing strongly diagonal behaviour for 1≤s≤12k(k+1)−13k+o(k). In particular, as k→∞, we confirm the main conjecture in Vinogradov's mean value theorem for 100% of the critical interval 1≤s≤12k(k+1)
Original languageEnglish
Pages (from-to)292-350
Number of pages59
JournalMathematika
Volume63
Issue number1
DOIs
Publication statusPublished - 2 Jan 2017

Keywords

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

Fingerprint

Dive into the research topics of 'Approximating the main conjecture in Vinogradov's mean value theorem'. Together they form a unique fingerprint.

Cite this