Title: A question proposed by K. Mahler on exceptional sets of transcendental functions with integer coefficients: solution of a Mahler's problem,
Abstract: In this paper, we shall prove that any subset of $\overline{\mathbb Q}\cap
B(0,1)$, which is closed under complex conjugation and which contains the
element $0$, is the exceptional set of uncountably many transcendental
functions, analytic in the unit ball, with integer coefficients. This solves a
strong version of an old question proposed by K. Mahler (1976).