On the Exceptional Set of Transcendental Entire Functions in Several Variables
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866913580638535680 |
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| author | Alves, Diego Lelis, Jean Marques, Diego Trojovský, Pavel |
| author_facet | Alves, Diego Lelis, Jean Marques, Diego Trojovský, Pavel |
| contents | In this paper, among other things, we prove that any subset of $\overline{\mathbb{Q}}^m$ (closed under complex conjugation and which contains the origin) is the exceptional set of uncountable many transcendental entire functions over $\mathbb{C}^m$ with rational coefficients. This result solves a several variables version of a question posed by Mahler for transcendental entire functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_03281 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the Exceptional Set of Transcendental Entire Functions in Several Variables Alves, Diego Lelis, Jean Marques, Diego Trojovský, Pavel Number Theory Complex Variables In this paper, among other things, we prove that any subset of $\overline{\mathbb{Q}}^m$ (closed under complex conjugation and which contains the origin) is the exceptional set of uncountable many transcendental entire functions over $\mathbb{C}^m$ with rational coefficients. This result solves a several variables version of a question posed by Mahler for transcendental entire functions. |
| title | On the Exceptional Set of Transcendental Entire Functions in Several Variables |
| topic | Number Theory Complex Variables |
| url | https://arxiv.org/abs/2306.03281 |