# 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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