%0 Journal Article
%T Sumsets of dense sets and sparse sets
%A John T. Griesmer
%J Mathematics
%D 2009
%I arXiv
%X R. Jin showed that whenever A and B are sets of integers having positive upper Banach density, the sumset A+B is piecewise syndetic. This result was strengthened by Bergelson, Furstenberg, and Weiss to conclude that A+B must be piecewise Bohr. We generalize the latter result to cases where A has Banach density 0, giving a new proof of the previous results in the process.
%U http://arxiv.org/abs/0911.2278v2