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A NOTE ON AN ASYMPTOTIC VERSION OF A PROBLEM OF MAHLER
Published online by Cambridge University Press: 15 September 2022
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.
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- Research Article
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- Copyright
- © The Author(s), 2022. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.
Footnotes
The authors are supported by National Council for Scientific and Technological Development, CNPq.