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Corpus ID: 52210230

Approximate Polynomial Structure in Additively Large Sets

@article{Nasso2016ApproximatePS,
title={Approximate Polynomial Structure in Additively Large Sets},
author={Mauro Di Nasso and Isaac Goldbring and Renling Jin and Steven C. Leth and Martino Lupini and Karl Mahlburg},
journal={Integers},
year={2016},
volume={16},
pages={A49}
}

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.

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In the past few decades, nonstandard methods, as a branch of mathematical logic, have been successfully applied to obtain new results in additive/combinatorial number theory (cf. [BJ, Ji1, Ji2, Ji3,… Expand