Diego Marques ; Elaine Silva - A Note on Transcendental Power Series Mapping the Set of Rational Numbers into Itself

cm:9459 - Communications in Mathematics, June 28, 2017, Volume 25 (2017), Issue 1 - https://doi.org/10.1515/cm-2017-0001
A Note on Transcendental Power Series Mapping the Set of Rational Numbers into ItselfArticle

Authors: 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].

    https://doi.org/10.1515/cm-2017-0001
    Source: HAL:hal-03664934v1
    Volume: Volume 25 (2017), Issue 1
    Published on: June 28, 2017
    Imported on: May 11, 2022
    Keywords: General Mathematics,[MATH]Mathematics [math]
    Licence: Attribution-Non Commercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)

    Classifications

    Mathematics Subject Classification 20201
    Sources:
    • [1] zbMATH Open.

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