Hasse norm principle for Galois dihedral extensions

Abstract

Let $L/k$ an Galois extension of number fields with Galois group isomorphic to a dihedral group of order $2n$. In this note, we give a general description of the Hasse norm principle for $L/k$ and the weak approximation for the norm one torus $R_{L/k}^1({\mathbb{G}}_m)$ associated to $L/k$.

arXiv comment5 pages