A Class Number Problem for the Cyclotomic $\mathbb{Z}_2$-extension of $\mathbb{Q}(\sqrt{5})$
Takuya Aoki · Tokyo Journal of Mathematics · 2016
Let $K_n$ be the $n$-th layer of the cyclotomic $\mathbb{Z}_2$-extension of $\mathbb{Q}(\sqrt{5})$ and $h_n$ the class number of $K_n$. We prove that, if $\ell$ is a prime number less than $6\cdot10^4$, then $\ell$ does not divide $h_n$ for any non-negative integer $n$.