Abstract
AbstractWe 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.
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