A note on the Freiman and Balog-Szemeredi-Gowers theorems in finite fields

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dc.creatorGreen, Ben
dc.creatorTao, Terence
dc.date2007-01-22
dc.date2007-11-12
dc.date.accessioned2026-07-07T08:42:01Z
dc.date.available2026-07-07T08:42:01Z
dc.descriptionWe obtain quantitative versions of the Balog-Szemeredi-Gowers and Freiman theorems in the model case of a finite field geometry F_2^n, improving the previously known bounds in such theorems. For instance, if A is a subset of F_2^n such that |A+A| <= K|A| (thus A has small additive doubling), we show that there exists an affine subspace V of F_2^n of cardinality |V| >> K^{-O(\sqrt{K})} |A| such that |A \cap V| >> |V|/2K. Under the assumption that A contains at least |A|^3/K quadruples with a_1 + a_2 + a_3 + a_4 = 0 we obtain a similar result, albeit with the slightly weaker condition |V| >> K^{-O(K)}|A|.
dc.description12 pages, to appear in J. Aust. Math. Society. Some very minor revisions from previous version
dc.identifierhttps://arxiv.org/abs/math/0701585
dc.identifierhttp://arxiv.org/abs/math/0701585
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/141854
dc.subjectCombinatorics
dc.subjectNumber Theory
dc.titleA note on the Freiman and Balog-Szemeredi-Gowers theorems in finite fields
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