New Bounds on cap sets

Details New Bounds on cap sets New Bounds on cap sets

2011-01-31

arxiv.org/abs/1101.5851v2

Mathematics

Classical Analysis and ODEs

New version: The most substantive change is the correction of our overstatement of the efficacy of the asymmetric Balog-Szemer

Scientific paper

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.

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