On the Bogolyubov–Ruzsa lemma

By Tom Sanders. 2010

199 citations recorded by the source corpus.

Our main result is that if A is a finite subset of an abelian group with |A+A| < K|A|, then 2A-2A contains an O(log^{O(1)} K)-dimensional coset progression M of size at least exp(-O(log^{O(1)} K))|A|.

Subfields: Discrete Mathematics and Combinatorics, Electrical and Electronic Engineering, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/52044be832497d8b3a71187ed6f8e6b168b9936f

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In Discrete Mathematics and Combinatorics

In Electrical and Electronic Engineering

In Geometry and Topology

Citations in the corpus

The structure of approximate groups (2011, background): “Again, see [47]; see also [24] for an earlier result in this direction.”
The structure theory of set addition revisited (2012, methodology): “his is the following conjecture. Conjecture 13.5. Suppose that n1,...,nk are natural numbers. Then ż ˇˇ ˇ ˇ ˇ ÿk i“1 expp2πin2 i θq ˇ ˇ ˇ ˇ ˇ 4 dθ“ Opk2`op1qq. Inserting ideas around Theorem 1.4 (see [San10]) into the work of [Cha04] (itself developed from an argument of Bourgain in [JL01]) yield th”
Growth in groups: ideas and perspectives (2013, unknown): “n a proper subﬁeld. The strength of this result must be underlined: Ais growing by a factor of |A|δ, where δ>0 is moreover independent of p. In contrast, even after impressive recent improvements ([San12]; see also [CS10]), the main additive-combinatorial result for abelian groups (Freiman’s theo”