Ambiguous Numbers over $P(\zeta_3)$ of Absolutely Abelian Extensions of Degree 6
Hisako Furuya · Tokyo Journal of Mathematics · 1982
2}$ when 3 unramifies in $K/P(\zeta_{\$})$ and it is $3^{2t-1}$ when 3 ramifies in $K/P(\zeta_{8})$ where $t+1$ is the number of prime numbers which ramify in $K/P$.Let $\Gamma$ be the genus field of $K/P$, then $\Gamma/K$ is unramified and the number of these ideal classes of $K$ which are principal in $\Gamma$ is a multiple of $(\Gamma:K)$ and it is larger than $(\Gamma:K)$ if $t\geqq 2$ .\S 1. Preliminaries.