157 citations · 642 across the 35 of their papers we have counts for
7 papers · 1 filter
Fourier uniformity on subspaces
Ben Green, Tom Sanders
Let be a fixed finite field, and let . It is a well-known fact that there is a subspace , $\mbox{codim} V \ll_δ 1$, and an…
Monochromatic sums and products
Ben Green, Tom Sanders
Suppose that is coloured with colours. Then there is some colour class containing at least quadruples of the form .
On certain other sets of integers
Tom Sanders
We show that if A is a subset of {1,...,N} containing no non-trivial three-term arithmetic progressions then |A|=O(N/ log^{3/4-o(1)} N).
Green's sumset problem at density one half
Tom Sanders
We investigate the size of subspaces in sumsets and show two main results. First, if A is a subset of F_2^n with density at least 1/2 - o(n^{-1/2}) then A+A contains a subspace of…
Three-term arithmetic progressions and sumsets
Tom Sanders
Suppose that G is an abelian group and A is a finite subset of G containing no three-term arithmetic progressions. We show that |A+A| >> |A|(log |A|)^{1/3-ε} for all ε>0.
A note on Freiman's theorem in vector spaces
Tom Sanders
We show that if A is a subset of F_2^n and |A+A| < K|A| then A is contained in a subspace of size at most 2^{O(K^{3/2}log K)}|A|. This improves on the previous best of 2^{O(K^2)}.