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arXiv · 2409.12936

Multiplicative recurrence of M\"obius transformations

Sun-Kai Leung·Christian Táfula
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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.

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Sun-Kai Leung, Christian Táfula. 2024-09-19. Multiplicative recurrence of M\"obius transformations. https://arxiv.org/abs/2409.12936

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