Sumsets of dense sets and sparse sets
Dynamical Systems
2010-11-02 v2 Number Theory
Abstract
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.
Keywords
Cite
@article{arxiv.0911.2278,
title = {Sumsets of dense sets and sparse sets},
author = {John T. Griesmer},
journal= {arXiv preprint arXiv:0911.2278},
year = {2010}
}
Comments
LaTeX, 19 Pages, major revision. Main proof simplified, references added. Accepted by Israel Journal of Mathematics