论文标题
$ 5 $ - 含义的五五首五级kummer扩展程序组
$5$-rank of ambiguous class groups of quintic Kummer extensions
论文作者
论文摘要
令$ k \，= \，\ mathbb {q}（\ sqrt [5] {n}，ζ_5）$，其中$ n $是一个正整数，$ 5^{th} $ power-wore-power-free，其$ 5- $ $ $ $ $ $ $ $ 5- $ class group tor Isomorphic tor Isomorphic to $ \ mathbb {z}/5 \ mathbb {z} \ times \ mathbb {z}/5 \ mathbb {z} $。令$ k_0 \，= \，\ mathbb {q}（ζ_5）$是包含一个原始$ 5^{th} $ unity $ζ_5$的$ 5^{th} $的环形字段。令$ c_ {k，5}^{（σ）} $在$ gal（k/k_0）$ = $<σ>$的动作下的模棱两可类别的组。本文的目的是确定所有整数$ n $，以便歧义类$ c_ {k，5}^{（σ）} $具有排名$ 1 $或$ 2 $。
Let $k \,=\, \mathbb{Q}(\sqrt[5]{n},ζ_5)$, where $n$ is a positive integer, $5^{th}$ power-free, whose $5-$class group is isomorphic to $\mathbb{Z}/5\mathbb{Z}\times\mathbb{Z}/5\mathbb{Z}$. Let $k_0\,=\,\mathbb{Q}(ζ_5)$ be the cyclotomic field containing a primitive $5^{th}$ root of unity $ζ_5$. Let $C_{k,5}^{(σ)}$ the group of the ambiguous classes under the action of $Gal(k/k_0)$ = $<σ>$. The aim of this paper is to determine all integers $n$ such that the group of ambiguous classes $C_{k,5}^{(σ)}$ has rank $1$ or $2$.
