English

Improved bound in Roth's theorem on arithmetic progressions

Number Theory 2020-05-05 v1

Abstract

We prove that if A{1,,N}A\subseteq \{1,\dots,N\} does not contain any non-trivial three-term arithmetic progression, then A(loglogN)3+o(1)logNN.|A|\ll \frac{(\log\log N)^{3+o(1)}}{\log N}N\,.

Keywords

Cite

@article{arxiv.2005.01145,
  title  = {Improved bound in Roth's theorem on arithmetic progressions},
  author = {Tomasz Schoen},
  journal= {arXiv preprint arXiv:2005.01145},
  year   = {2020}
}
R2 v1 2026-06-23T15:16:36.130Z