Approximate polynomial structure in additively large sets
Combinatorics
2016-10-24 v1 Logic
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.
Cite
@article{arxiv.1508.02350,
title = {Approximate polynomial structure in additively large sets},
author = {Mauro Di Nasso and Isaac Goldbring and Renling Jin and Steven Leth and Martino Lupini and Karl Mahlburg},
journal= {arXiv preprint arXiv:1508.02350},
year = {2016}
}
Comments
10 pages