English

Sum-product phenomena for Ahlfors-regular sets

Classical Analysis and ODEs 2025-08-01 v3 Combinatorics Metric Geometry

Abstract

We utilise the recent work of Orponen to yield a sum-product result for Ahlfors-regular sets. As a corollary, we obtain the fractal analogue of Solymosi's 4/34/3-bound for finite subsets of R.\mathbb{R}.

Keywords

Cite

@article{arxiv.2501.02131,
  title  = {Sum-product phenomena for Ahlfors-regular sets},
  author = {William O'Regan},
  journal= {arXiv preprint arXiv:2501.02131},
  year   = {2025}
}

Comments

10 pages, previous version contained a gap, see remark 1.6

R2 v1 2026-06-28T20:55:56.545Z