Number fields with prescribed norms

Abstract: Let $G$ be a finite abelian group, let $k$ be a number field, and let $\alpha\in k^\times$. We count Galois extensions $K/k$ with Galois group $G$ such that $\alpha$ is a norm from $K/k$. In particular, we show that such extensions always exist. This is joint work with Christopher Frei and Daniel Loughran.

number theory

Audience: researchers in the topic

London number theory seminar

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