Near optimal bounds in Freiman's theorem

@article{Schoen2011NearOB,
  title={Near optimal bounds in Freiman's theorem},
  author={Tomasz Schoen},
  journal={Duke Mathematical Journal},
  year={2011},
  volume={158},
  pages={1-12}
}
  • T. Schoen
  • Published 15 May 2011
  • Mathematics
  • Duke Mathematical Journal
We prove that if for a finite set A of integers we have |A+A| ≤ K|A|, then A is contained in a generalized arithmetic progression of dimension at most K −1/2 and size at most exp(K −1/2 )|A| for some absolute constant C. We also discuss a number of applications of this result. 
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