Abstract
Abstract
We prove that for any infinite sets of nonnegative integers
$\mathcal {A}$
and
$\mathcal {B}$
, there exist transcendental analytic functions
$f\in \mathbb {Z}\{z\}$
whose coefficients vanish for any indexes
$n\not \in \mathcal {A}+\mathcal {B}$
and for which
$f(z)$
is algebraic whenever z is algebraic and
$|z|<1$
. As a consequence, we provide an affirmative answer for an asymptotic version of Mahler’s problem A.
Publisher
Cambridge University Press (CUP)