Algebraic periodic points of transcendental entire functions
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866912128136380416 |
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| author | Krumm, David Marques, Diego Moreira, Carlos Gustavo Trojovský, Pavel |
| author_facet | Krumm, David Marques, Diego Moreira, Carlos Gustavo Trojovský, Pavel |
| contents | We prove the existence of transcendental entire functions $f$ having a property studied by Mahler, namely that $f(\overline{\mathbb{Q}})\subseteq \overline{\mathbb{Q}}$ and $f^{-1}(\overline{\mathbb{Q}})\subseteq \overline{\mathbb{Q}}$, and in addition having a prescribed number of $k$-periodic algebraic orbits, for all $k\geq 1$. Under a suitable topology, such functions are shown to be dense in the set of all entire transcendental functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_09614 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Algebraic periodic points of transcendental entire functions Krumm, David Marques, Diego Moreira, Carlos Gustavo Trojovský, Pavel Number Theory Primary 37P10, Secondary 11Jxx We prove the existence of transcendental entire functions $f$ having a property studied by Mahler, namely that $f(\overline{\mathbb{Q}})\subseteq \overline{\mathbb{Q}}$ and $f^{-1}(\overline{\mathbb{Q}})\subseteq \overline{\mathbb{Q}}$, and in addition having a prescribed number of $k$-periodic algebraic orbits, for all $k\geq 1$. Under a suitable topology, such functions are shown to be dense in the set of all entire transcendental functions. |
| title | Algebraic periodic points of transcendental entire functions |
| topic | Number Theory Primary 37P10, Secondary 11Jxx |
| url | https://arxiv.org/abs/2305.09614 |