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Communications in Mathematics

Editor-in-Chief: Rossi, Olga

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Mathematical Citation Quotient (MCQ) 2016: 0.28

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

Diego Marques / Elaine Silva
Published Online: 2017-06-28 | DOI: https://doi.org/10.1515/cm-2017-0001


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].

Keywords: Liouville numbers; Mahler’s question; power series


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About the article

Received: 2015-11-27

Accepted: 2016-07-14

Published Online: 2017-06-28

Published in Print: 2017-06-27

Citation Information: Communications in Mathematics, Volume 25, Issue 1, Pages 1–4, ISSN (Online) 2336-1298, DOI: https://doi.org/10.1515/cm-2017-0001.

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© 2017. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License. BY-NC-ND 4.0

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