On the Exceptional Set of Transcendental Entire Functions in Several Variables
Number Theory
2024-11-20 v1 Complex Variables
Abstract
In this paper, among other things, we prove that any subset of (closed under complex conjugation and which contains the origin) is the exceptional set of uncountable many transcendental entire functions over with rational coefficients. This result solves a several variables version of a question posed by Mahler for transcendental entire functions.
Keywords
Cite
@article{arxiv.2306.03281,
title = {On the Exceptional Set of Transcendental Entire Functions in Several Variables},
author = {Diego Alves and Jean Lelis and Diego Marques and Pavel Trojovský},
journal= {arXiv preprint arXiv:2306.03281},
year = {2024}
}