English

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.

Keywords

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

R2 v1 2026-06-22T10:30:19.463Z