Mean value estimates for odd cubic Weyl sums

Trevor D. Wooley

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

8 Citations (Scopus)
287 Downloads (Pure)

Abstract

We establish an essentially optimal estimate for the ninth moment of the exponential sum having argument $\alpha x^3+\beta x$. The first substantial advance in this topic for over 60 years, this leads to improvements in Heath-Brown's variant of Weyl's inequality, and other applications of Diophantine type.
Original languageEnglish
Pages (from-to)946-957
Number of pages12
JournalBulletin of the London Mathematical Society
Volume47
Issue number6
Early online date20 Oct 2015
DOIs
Publication statusPublished - Dec 2015

Keywords

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

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