Geodesic
A Note on Transcendental Power Series Mapping the Set of Rational Numbers into Itself
Communications in Mathematics, Tome 25 (2017) no. 1, pp. 1-4

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

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 $F(z)\in \mathbb{Z} [z]$.
Classification : 11J81
Keywords: Liouville numbers; Mahler's question; power series 
@article{COMIM_2017__25_1_a0,
     author = {Marques, Diego and Silva, Elaine},
     title = {A {Note} on {Transcendental} {Power} {Series} {Mapping} the {Set} of {Rational} {Numbers} into {Itself}},
     journal = {Communications in Mathematics},
     pages = {1--4},
     publisher = {mathdoc},
     volume = {25},
     number = {1},
     year = {2017},
     mrnumber = {3667071},
     zbl = {06888083},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/COMIM_2017__25_1_a0/}
}
TY  - JOUR
AU  - Marques, Diego
AU  - Silva, Elaine
TI  - A Note on Transcendental Power Series Mapping the Set of Rational Numbers into Itself
JO  - Communications in Mathematics
PY  - 2017
SP  - 1
EP  - 4
VL  - 25
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/COMIM_2017__25_1_a0/
LA  - en
ID  - COMIM_2017__25_1_a0
ER  - 
%0 Journal Article
%A Marques, Diego
%A Silva, Elaine
%T A Note on Transcendental Power Series Mapping the Set of Rational Numbers into Itself
%J Communications in Mathematics
%D 2017
%P 1-4
%V 25
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/COMIM_2017__25_1_a0/
%G en
%F COMIM_2017__25_1_a0
Marques, Diego; Silva, Elaine. A Note on Transcendental Power Series Mapping the Set of Rational Numbers into Itself. Communications in Mathematics, Tome 25 (2017) no. 1, pp. 1-4. http://geodesic.mathdoc.fr/item/COMIM_2017__25_1_a0/