157 citations · 642 across the 35 of their papers we have counts for
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math.CA2010★ 157 cited
On the Bogolyubov-Ruzsa lemma
Tom Sanders
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(-…
math.CA2010★ 93 cited
On Roth's theorem on progressions
Tom Sanders
We show that if A is a subset of {1,...,N} contains no non-trivial three-term arithmetic progressions then |A|=O(N/ log^{1-o(1)} N). The approach is somewhat different from that us…