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arXiv · 2308.10245

Note on the Theorem of Balog, Szemerédi, and Gowers

Christian Reiher·Tomasz Schoen
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Abstract

We prove that every additive set $A$ with energy $E(A)\ge |A|^3/K$ has a subset $A'\subseteq A$ of size $|A'|\ge (1-\varepsilon)K^{-1/2}|A|$ such that $|A'-A'|\le O_\varepsilon(K^{4}|A'|)$. This is, essentially, the largest structured set one can get in the Balog-Szemerédi-Gowers theorem.

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Christian Reiher, Tomasz Schoen. 2024-02-18. Note on the Theorem of Balog, Szemerédi, and Gowers. https://doi.org/10.1007/s00493-024-00092-5

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