New bounds in Balog-Szemerédi-Gowers theorem

Abstract

We prove, in particular, that every finite subset A of an abelian group with the additive energy κ|A|3 contains a set A′ such that |A′|≫κ|A| and |A′ − A′|≪κ −4|A′|.

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Correspondence to Tomasz Schoen.

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The author is supported by NCN grant 2012/07/B/ST1/03556.

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Schoen, T. New bounds in Balog-Szemerédi-Gowers theorem. Combinatorica 35, 695–701 (2015). https://doi.org/10.1007/s00493-014-3077-4

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Mathematics Subject Classication (2000)

  • 11B75
  • 11P99