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arXiv · 0901.1335

Some field theoretical properties and an application concerning transcendental numbers

Christian Jensen·Diego Marques
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Abstract

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 $\QQ$.

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Christian Jensen, Diego Marques. 2009-01-09. Some field theoretical properties and an application concerning transcendental numbers. https://arxiv.org/abs/0901.1335

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