# Mean value estimates for odd cubic Weyl sums

Trevor D. Wooley

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

8 Citations (Scopus)

## 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 language English 946-957 12 Bulletin of the London Mathematical Society 47 6 20 Oct 2015 https://doi.org/10.1112/blms/bdv066 Published - Dec 2015

• math.NT
• 11L15
• 11L07
• 11P55