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 . 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.
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}
}