论文标题
$ \ mathbb {q}（\ sqrt [3] {p}）$的$ 3 $ -CLASS组及其正常关闭
The $3$-class groups of $\mathbb{Q}(\sqrt[3]{p})$ and its normal closure
论文作者
论文摘要
We determine the $3$-class groups of $\mathbb{Q}(\sqrt[3]{p})$ and $K=\mathbb{Q}(\sqrt[3]{p},\sqrt{-3})$ when $p\equiv 4,7\bmod 9$ is a prime and $3$ is a cubic modulo $p$.这证实了Barrucand-Cohn的猜想，并证明了Lemmermeyer在$ 3美元的$ k $中的最后剩下的案例。
We determine the $3$-class groups of $\mathbb{Q}(\sqrt[3]{p})$ and $K=\mathbb{Q}(\sqrt[3]{p},\sqrt{-3})$ when $p\equiv 4,7\bmod 9$ is a prime and $3$ is a cubic modulo $p$. This confirms a conjecture made by Barrucand-Cohn, and proves the last remaining case of a conjecture of Lemmermeyer on the $3$-class group of $K$.
