On exceptional sets of transcendental functions with integer coefficients: solution of a problem of Mahler
Volume 192 / 2020
Acta Arithmetica 192 (2020), 313-327
MSC: Primary 11Jxx; Secondary 30Dxx.
DOI: 10.4064/aa180326-13-2
Published online: 29 November 2019
Abstract
We prove that any subset of $\overline {\mathbb Q }\cap B(0,1)$ which is closed under complex conjugation and contains $0$ is the exceptional set of uncountably many transcendental functions, analytic in the unit ball, with integer coefficients. This strengthens a result of Mahler (1965) and answers a strong variant of an old question also proposed by Mahler (1976).
