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Keywords:
Liouville numbers; Mahler's question; power series
Liouville numbers; Mahler's question; power series
Summary:
In this note, we prove that there is no transcendental entire function $f(z)\in \mathbb{Q} [[z]]$ such that $f(\mathbb{Q} )\subseteq \mathbb{Q}$ and $\mathop{\rm den} f(p/q)=F(q)$, for all sufficiently large $q$, where $F(z)\in \mathbb{Z} [z]$.
References:
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