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A Note on Transcendental Power Series Mapping the Set of Rational Numbers into Itself

Diego Marques; Elaine Silva — 2017

Communications in Mathematics

In this note, we prove that there is no transcendental entire function $f (z) \in ℚ [[z]]$ such that $f (ℚ) \subseteq ℚ$ and $den f (p / q) = F (q)$ , for all sufficiently large $q$ , where $F (z) \in ℤ [z]$ .

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