On simple families of cyclic polynomials
On simple families of cyclic polynomials
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关于循环多项式的简单族
DOI：
10.1090/s0002-9939-02-06414-6
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发表时间：
2002
影响因子：
0.6
通讯作者：
Yuichi Rikuna
中科院分区：
文献类型：
--
作者：
Yuichi Rikuna
研究了有理函数域上循环扩张的多项式，其中一个变量满足一定的条件。利用它们，我们构造了代数数域上的循环多项式族。这些族给出了非Kummer（或非Artin-Schreier）循环扩张。在本文中，我们看到我们的多项式有两个很好的算术性质。一个是简单：我们的多项式及其判别式比Dentzer（1995），Malle and Mazat（1999）和Smith（1991）等已有的结果有更简单的表达式.另一个是一个系统性质：如果我们的多项式f之一给出扩张L/K，那么对于每个中间域M，我们可以很容易地从f系统地找到给出M/K的多项式.
We study polynomials giving cyclic extensions over rational function fields with one variable satisfying some conditions. By using them, we construct families of cyclic polynomials over some algebraic number fields. And these families give non-Kummer (or non-Artin-Schreier) cyclic extensions. In this paper, we see that our polynomials have two nice arithmetic properties. One is simplicity: our polynomials and their discriminants have more simple expressions than previous results, e.g. Dentzer (1995), Malle and Mazat (1999) and Smith (1991), etc. The other is a systematic property: if one of our polynomials f gives an extension L/K, then for every intermediate field M we can easily find polynomials giving M/K from f systematically.