A Note on Transcendental Power Series Mapping the Set of Rational Numbers into Itself
Communications in Mathematics (2017)
- Volume: 25, Issue: 1, page 1-4
- ISSN: 1804-1388
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topMarques, Diego, and Silva, Elaine. "A Note on Transcendental Power Series Mapping the Set of Rational Numbers into Itself." Communications in Mathematics 25.1 (2017): 1-4. <http://eudml.org/doc/294125>.
@article{Marques2017,
abstract = {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 $F(z)\in \mathbb \{Z\} [z]$.},
author = {Marques, Diego, Silva, Elaine},
journal = {Communications in Mathematics},
keywords = {Liouville numbers; Mahler's question; power series},
language = {eng},
number = {1},
pages = {1-4},
publisher = {University of Ostrava},
title = {A Note on Transcendental Power Series Mapping the Set of Rational Numbers into Itself},
url = {http://eudml.org/doc/294125},
volume = {25},
year = {2017},
}
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
PB - University of Ostrava
VL - 25
IS - 1
SP - 1
EP - 4
AB - 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 $F(z)\in \mathbb {Z} [z]$.
LA - eng
KW - Liouville numbers; Mahler's question; power series
UR - http://eudml.org/doc/294125
ER -
References
top- Mahler, K., 10.1017/S1446788700025866, J. Austral. Math. Soc., 5, 1965, 56-64, (1965) Zbl0148.27703MR0190094DOI10.1017/S1446788700025866
- Mahler, K., 10.1017/S0004972700021316, Bull. Austral. Math. Soc., 29, 1984, 101-108, (1984) Zbl0517.10001MR0732177DOI10.1017/S0004972700021316
- Maillet, E., Introduction à la Théorie des Nombres Transcendants et des Propriétés Arithmétiques des Fonctions, 1906, Gauthier-Villars, Paris, (1906)
- Marques, D., Moreira, C.G., 10.1017/S0004972714000471, Bull. Austral. Math. Soc., 91, 2015, 29-33, (2015) Zbl1308.11069MR3294255DOI10.1017/S0004972714000471
- Marques, D., Ramirez, J., 10.3792/pjaa.91.25, Proc. Japan Acad. Ser. A Math. Sci., 91, 2015, 25-28, (2015) Zbl1311.11067MR3310967DOI10.3792/pjaa.91.25
- Marques, D., Ramirez, J., Silva, E., A note on lacunary power series with rational coefficients, Bull. Austral. Math. Soc., 93, 2015, 1-3, (2015) MR3491477
- Marques, D., Schleischitz, J., 10.1017/S1446788715000415, J. Austral. Math. Soc., 100, 2016, 86-107, (2016) Zbl1335.11053MR3436773DOI10.1017/S1446788715000415
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