论文标题
以2美元的循环立方田塔的启发式学
Heuristics for $2$-class Towers of Cyclic Cubic Fields
论文作者
论文摘要
我们考虑最大$ 2 $ 2 $ extension $ k $的Galois Group $ g_2（k）$，其中$ k/\ mathbb {q} $是$ 3 $的循环。我们还考虑了$ g^+_ 2（k）$，其中无限允许进行分支。本着Cohen-Lenstra启发式方法的精神，我们将某些类型的Pro-2 $组确定为自然空间，其中$ g_2（k）$和$ g^+_ 2（k）$ live当$ 2 $ k $的$ 2 $ k $ as 2 $ $ 2 $时。尽管我们没有分配概率的理论方案，但我们提出数据并就此类组的分布进行一些观察和猜想。
We consider the Galois group $G_2(K)$ of the maximal unramified $2$-extension of $K$ where $K/\mathbb{Q}$ is cyclic of degree $3$. We also consider the group $G^+_2(K)$ where ramification is allowed at infinity. In the spirit of the Cohen-Lenstra heuristics, we identify certain types of pro-$2$ group as the natural spaces where $G_2(K)$ and $G^+_2(K)$ live when the $2$-class group of $K$ is $2$-generated. While we do not have a theoretical scheme for assigning probabilities, we present data and make some observations and conjectures about the distribution of such groups.
