Some field theoretical properties and an application concerning transcendental numbers

Details Some field theoretical properties and an application concerning transcendental numbers Some field theoretical properties and an application concerning transcendental numbers

2009-01-09

arxiv.org/abs/0901.1335v3

Journal of Algebra and its Applications, v9, 493-500, 2010

Mathematics

Number Theory

7 pages

Scientific paper

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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