Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Some field theoretical properties and an application concerning
  transcendental numbers   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 $\QQ$.

9
The categories of this paper are: nlin
36
The categories of this paper are: cmp-lg
3
The categories of this paper are: physics
13
The categories of this paper are: quant-ph
5
The categories of this paper are: gr-qc
30
The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat
14
The categories of this paper are: math-ph
1
The categories of this paper are: cs
32
The categories of this paper are: atom-ph
33
The categories of this paper are: plasm-ph
37
The categories of this paper are: supr-con
16
The categories of this paper are: stat
22
The categories of this paper are: chao-dyn
27
The categories of this paper are: comp-gas
24
The categories of this paper are: dg-ga