Vol. 5, No. 3, 2012

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On the Bogolyubov–Ruzsa lemma

Tom Sanders

Vol. 5 (2012), No. 3, 627–655
Abstract

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(logO(1)2K)-dimensional coset progression M of size at least exp(O(logO(1)2K))|A|.

Keywords
Freiman, Fourier analysis, sumsets, generalised arithmetic progressions, coset progressions, small doubling
Mathematical Subject Classification 2010
Primary: 11L07
Milestones
Received: 4 November 2010
Revised: 12 September 2011
Accepted: 9 October 2011
Published: 15 October 2012
Authors
Tom Sanders
Department of Pure Mathematics and Mathematical Statistics
University of Cambridge
Wilberforce Road
Cambridge
CB3 0WB
United Kingdom