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arXiv · 2306.03281

On the Exceptional Set of Transcendental Entire Functions in Several Variables

Diego Alves·Jean Lelis·Diego Marques·Pavel Trojovský
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Abstract

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.

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Diego Alves, Jean Lelis, Diego Marques, Pavel Trojovský. 2023-06-05. On the Exceptional Set of Transcendental Entire Functions in Several Variables. https://doi.org/10.1017/s0004972723001041

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