English

Hotspot lemmas for non-compact spaces

Dynamical Systems 2019-12-24 v1 Number Theory

Abstract

We extend the hotspot lemma, or Piatetski\u{i}-Shapiro normality criterion, to dynamical systems on non-compact spaces. We build on the work of N. G. Moshchevitin and I. D. Shkredov, noting an issue in some of their proofs, and adding a necessary and sufficient condition to remove this issue.

Cite

@article{arxiv.1912.10265,
  title  = {Hotspot lemmas for non-compact spaces},
  author = {Dylan Airey and Bill Mance},
  journal= {arXiv preprint arXiv:1912.10265},
  year   = {2019}
}

Comments

4 pages

R2 v1 2026-06-23T12:53:23.859Z