A note on transcendental entire functions mapping uncountable many Liouville numbers into the set of Liouville numbers

Proceedings of the Japan Academy, Series A. Mathematical Sciences

article

Jean Lelis¹  Diego Marques¹  Josimar Ramirez² 

[1] Universidade de Braslia, Campus Universita´rio Darcy Ribeiro;Universidade Federal de Uberlaˆndia, Campus Santa Moˆnica

关键词: Finite difference method;    nonlinear partial differential equations;    Cauchy problem;    ill-posed problems.;   

DOI  :  10.3792/pjaa.93.111

学科分类：数学（综合）

来源: Japan Academy

【 摘 要 】

In 1906, Maillet proved that given a non-constant rational function $f$, with rational coefficients, if $\xi$ is a Liouville number, then so is $f(\xi)$. Motivated by this fact, in 1984, Mahler raised the question about the existence of transcendental entire functions with this property. In this work, we define an uncountable subset of Liouville numbers for which there exists a transcendental entire function taking this set into the set of the Liouville numbers.

【 授权许可】

Unknown