English

Bounds for the Cubic Weyl Sum

Number Theory 2009-05-13 v1

Abstract

It is shown, subject to the abc-conjecture, that nNexp(2πiαn3)ϵ,αN5/7+ϵ\sum_{n\le N}\exp(2\pi i\alpha n^3)\ll_{\epsilon,\alpha}N^{5/7+\epsilon} for any ϵ>0\epsilon>0 and any quadratic irrational α\alpha.

Keywords

Cite

@article{arxiv.0905.1869,
  title  = {Bounds for the Cubic Weyl Sum},
  author = {D. R. Heath-Brown},
  journal= {arXiv preprint arXiv:0905.1869},
  year   = {2009}
}
R2 v1 2026-06-21T13:01:14.169Z