Some results on asymptotic versions of Mahler's problems
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866909508149706752 |
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| author | Francisco, Ricardo Marques, Diego |
| author_facet | Francisco, Ricardo Marques, Diego |
| contents | In this paper, we show the existence of a transcendental function $f\in\mathbb{Z}\{z\}$ with coefficients that are almost all bounded such that $f$ and all its derivatives assume algebraic values at algebraic points. Furthermore, we demonstrate that certain subsets of algebraic numbers are exceptional sets of some transcendental function $f\in\mathbb{Z}\{z\}$ with almost all bounded coefficients. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_17090 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Some results on asymptotic versions of Mahler's problems Francisco, Ricardo Marques, Diego Number Theory 11J81, 30B10 In this paper, we show the existence of a transcendental function $f\in\mathbb{Z}\{z\}$ with coefficients that are almost all bounded such that $f$ and all its derivatives assume algebraic values at algebraic points. Furthermore, we demonstrate that certain subsets of algebraic numbers are exceptional sets of some transcendental function $f\in\mathbb{Z}\{z\}$ with almost all bounded coefficients. |
| title | Some results on asymptotic versions of Mahler's problems |
| topic | Number Theory 11J81, 30B10 |
| url | https://arxiv.org/abs/2502.17090 |