On transcendental analytic functions mapping an uncountable class of $U$-numbers into Liouville numbers

Proceedings of the Japan Academy, Series A. Mathematical Sciences

article

Diego Marques¹  Josimar Ramirez¹ 

[1] Universidade de Braslia, Campus Universita´rio Darcy Ribeiro

关键词: Transcendental functions;    m-ultra number;    Liouville;    height.;   

DOI  :  10.3792/pjaa.91.25

学科分类：数学（综合）

来源: Japan Academy

【 摘 要 】

In this paper, we shall prove, for any $m\geq 1$, the existence of an uncountable subset of $U$-numbers of type $\leq m$ (which we called the set of \textit{$m$-ultra numbers}) for which there exists uncountably many transcendental analytic functions mapping it into Liouville numbers.

【 授权许可】

Unknown