Abstract
Abstract
We prove that any subset of
$\overline {\mathbb {Q}}^m$
(closed under complex conjugation and which contains the origin) is the exceptional set of uncountably 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 [Lectures on Transcendental Numbers, Lecture Notes in Mathematics, 546 (Springer-Verlag, Berlin, 1976)].
Publisher
Cambridge University Press (CUP)