Type: Article
Publication Date: 2011-11-30
Citations: 71
DOI: https://doi.org/10.1090/s0894-0347-2011-00725-x
We provide an improvement over Meshulam's bound on cap sets in $F_3^N$. We show that there exist universal $\epsilon >0$ and $C>0$ so that any cap set in $F_3^N$ has size at most $C {3^N \over N^{1+\epsilon }}$. We do this by obtaining quite strong information about the additive combinatorial properties of the large spectrum.