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arXiv · 0911.2278

Sumsets of dense sets and sparse sets

John T. Griesmer
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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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John T. Griesmer. 2009-11-12. Sumsets of dense sets and sparse sets. https://arxiv.org/abs/0911.2278

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