A Note on Transcendental Power Series Mapping the Set of Rational Numbers into Itself
Authors: Diego Marques ; Elaine Silva
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Diego Marques;Elaine Silva
In this note, we prove that there is no transcendental entire function f(z) ∈ ℚ[[z]] such that f(ℚ) ⊆ ℚ and den f(p/q) = F(q), for all sufficiently large q, where F(z) ∈ ℤ[z].
Lelis, Jean; Marques, Diego, 2020, On Transcendental Entire Functions Mapping Q Into Itself, Journal Of Number Theory, 206, pp. 310-319, 10.1016/j.jnt.2019.06.018.