# 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} }

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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