Multiplicative recurrence of Möbius transformations
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909663726927872 |
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| author | Leung, Sun-Kai Táfula, Christian |
| author_facet | Leung, Sun-Kai Táfula, Christian |
| contents | We establish a complete characterization of multiplicative recurrence for images of the positive integers under Möbius 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_12936 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Multiplicative recurrence of Möbius transformations Leung, Sun-Kai Táfula, Christian Number Theory Combinatorics Dynamical Systems 05C15, 05C69, 05D10, 11B30, 37A44 We establish a complete characterization of multiplicative recurrence for images of the positive integers under Möbius 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. |
| title | Multiplicative recurrence of Möbius transformations |
| topic | Number Theory Combinatorics Dynamical Systems 05C15, 05C69, 05D10, 11B30, 37A44 |
| url | https://arxiv.org/abs/2409.12936 |