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

Diego Marques; Josimar Ramirez

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

Number Theory 2014-09-01 v2

Authors: Diego Marques , Josimar Ramirez

Abstract

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 {\it $m$ -ultra numbers}) for which there exists uncountably many transcendental analytic functions mapping it into Liouville numbers.

Keywords

transcendental analytic functions $U$-numbers Liouville numbers $m$-ultra numbers uncountable sets diophantine approximation

Cite

@article{arxiv.1408.0844,
  title  = {On transcendental analytic functions mapping an uncountable class of $U$-numbers into Liouville numbers},
  author = {Diego Marques and Josimar Ramirez},
  journal= {arXiv preprint arXiv:1408.0844},
  year   = {2014}
}

Comments

9 pages, no figure (Submitted)

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