English

Mean value estimates for odd cubic Weyl sums

Number Theory 2022-11-22 v1

Abstract

We establish an essentially optimal estimate for the ninth moment of the exponential sum having argument αx3+βx\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.

Keywords

Cite

@article{arxiv.1401.7152,
  title  = {Mean value estimates for odd cubic Weyl sums},
  author = {Trevor D. Wooley},
  journal= {arXiv preprint arXiv:1401.7152},
  year   = {2022}
}
R2 v1 2026-06-22T02:56:12.282Z