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arXiv · 1912.10265

Hotspot lemmas for non-compact spaces

Dylan Airey·Bill Mance
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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.

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Dylan Airey, Bill Mance. 2019-12-21. Hotspot lemmas for non-compact spaces. https://arxiv.org/abs/1912.10265

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