Transcendence of Hecke-Mahler Series
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866917871621242880 |
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| author | Luca, Florian Ouaknine, Joel Worrell, James |
| author_facet | Luca, Florian Ouaknine, Joel Worrell, James |
| contents | We prove transcendence of the Hecke-Mahler series $\sum_{n=0}^\infty f(\lfloor nθ+α\rfloor) β^{-n}$, where $f(x) \in \mathbb{Z}[x]$ is a non-constant polynomial $α$ is a real number, $θ$ is an irrational real number, and $β$ is an algebraic number such that $|β|>1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_07908 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Transcendence of Hecke-Mahler Series Luca, Florian Ouaknine, Joel Worrell, James Number Theory Formal Languages and Automata Theory 11J87 We prove transcendence of the Hecke-Mahler series $\sum_{n=0}^\infty f(\lfloor nθ+α\rfloor) β^{-n}$, where $f(x) \in \mathbb{Z}[x]$ is a non-constant polynomial $α$ is a real number, $θ$ is an irrational real number, and $β$ is an algebraic number such that $|β|>1$. |
| title | Transcendence of Hecke-Mahler Series |
| topic | Number Theory Formal Languages and Automata Theory 11J87 |
| url | https://arxiv.org/abs/2412.07908 |