Roth’s theorem on progressions revisited

@article{Bourgain2008RothsTO,
  title={Roth’s theorem on progressions revisited},
  author={J. Bourgain},
  journal={Journal d'Analyse Math{\'e}matique},
  year={2008},
  volume={104},
  pages={155-192}
}
  • J. Bourgain
  • Published 2008
  • Mathematics
  • Journal d'Analyse Mathématique
This paper is a sequel to [B]. Our main result is an improvement of the density condition for a subset A ⊂ {1,. .. , N } to contain a nontrivial arithmetic progression of length 3. More specifically, we prove the following Theorem 1. (0.1) δ ≫ (log log N) 2 (log N) 2/3 (N assumed sufficiently large), then A contains nontrivial progressions of length 3. 
105 Citations
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