M. Allen

Counting metacyclic fields

By a metacyclic field $K$ we mean the Galois closure of a pure field $\mathbb{Q}(\sqrt[\ell]{D})$, $D\in\mathbb{Z}$, of odd prime degree $\ell$. Let $\mathcal{M}_\ell$ denote the collection of isomorphism classes of metacyclic fields of degree $\ell(\ell-1)$. Write $N_\ell(X)=\#\{K\in\mathcal{M}_\ell: |\Delta_K|\leq X\...