Multiplicative recurrence of M\"obius transformations
Number Theory
2025-07-01 v3 Combinatorics
Dynamical Systems
Abstract
We establish a complete characterization of multiplicative recurrence for images of the positive integers under M\"obius transformations, answering a question of Donoso--Le--Moreira--Sun in the negative. As a consequence, we strengthen and extend a Diophantine approximation result of Charamaras--Mountakis--Tsinas, confirming their conjectures.
Cite
@article{arxiv.2409.12936,
title = {Multiplicative recurrence of M\"obius transformations},
author = {Sun-Kai Leung and Christian Táfula},
journal= {arXiv preprint arXiv:2409.12936},
year = {2025}
}
Comments
13 pages. We answer a question of Donoso--Le--Moreira--Sun in the negative, correcting our earlier claim