English

A polylogarithmic bound in the nonlinear Roth theorem

Number Theory 2023-01-09 v2 Combinatorics

Abstract

We show that sets of integers lacking the configuration xx, x+yx+y, x+y2x+y^2 have at most polylogarithmic density.

Keywords

Cite

@article{arxiv.2003.04122,
  title  = {A polylogarithmic bound in the nonlinear Roth theorem},
  author = {Sarah Peluse and Sean Prendiville},
  journal= {arXiv preprint arXiv:2003.04122},
  year   = {2023}
}

Comments

v2. Replaced use of Hahn-Banach theorem with simplified treatment involving Cauchy-Schwarz

R2 v1 2026-06-23T14:08:44.952Z