%0 Journal Article
%T Some field theoretical properties and an application concerning transcendental numbers
%A Christian Jensen
%A Diego Marques
%J Mathematics
%D 2009
%I arXiv
%X For a proper subfield $K$ of $\QQ$ we show the existence of an algebraic number $\alpha$ such that no power $\alpha^n$, $n\geq 1$, lies in $K$. As an application it is shown that these numbers, multiplied by convenient Gaussian numbers, can be written in the form $P(T)^{Q(T)}$ for some transcendental numbers $T$ where $P$ and $Q$ are arbitrarily prescribed non-constant rational functions over $\QQ$.
%U http://arxiv.org/abs/0901.1335v3