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Preprint Number 902

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902. Mauro Di Nasso, Isaac Goldbring, Renling Jin, Steven Leth, Martino Lupini, and Karl Mahlburg
Approximate polynomial structure in additively large sets
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Submission date: 10 August 2015.

Abstract:

We show that any subset of the natural numbers with positive logarithmic Banach density contains a set that is within a factor of two of a geometric progression, improving the bound on a previous result of the authors. Density conditions on subsets of the natural numbers that imply the existence of approximate powers of arithmetic progressions are developed and explored.

Mathematics Subject Classification:

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Full text arXiv 1508.02350: pdf, ps.


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