SOME FIELD THEORETIC PROPERTIES AND AN APPLICATION CONCERNING TRANSCENDENTAL NUMBERS

被引：4

作者：

Jensen, Christian U. ^{[1
]}

Marques, Diego ^{[2
]}

机构：

[1] Univ Copenhagen, Dept Math Sci, Copenhagen, Denmark

[2] Univ Brasilia, Dept Matemat, Brasilia, DF, Brazil

来源：

JOURNAL OF ALGEBRA AND ITS APPLICATIONS | 2010年 / 9卷 / 03期

关键词：

Artin-Schreier; Galois theory; Gelfond-Schneider; transcendental numbers;

D O I：

10.1142/S0219498810004038

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

For a proper subfield K of Q we show the existence of an algebraic number alpha such that no power alpha(n), n >= 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 nonconstant rational functions over (Q) over bar.

引用

页码：493 / 500

页数：8

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