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Sumsets of dense sets and sparse sets

Authors
  • Griesmer, John T.
Type
Preprint
Publication Date
Nov 01, 2010
Submission Date
Nov 11, 2009
Source
arXiv
License
Yellow
External links

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.

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