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arXiv · 2502.00526

Dirichlet's Lemma in Number Fields

Franz Lemmermeyer
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Abstract

Dirichlet's Lemma states that every primitive quadratic Dirichlet character $χ$ can be written in the form $χ(n) = (\fracΔn)$ for a suitable quadratic discriminant $Δ$. In this article we define a group, the separant class group, that measures the extent to which Dirichlet's Lemma fails in general number fields $F$. As an application we will show that over fields with trivial separant class groups, genus theory of quadratic extensions can be made as explicit as over the rationals.

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BibTeXRIS

Franz Lemmermeyer. 2026-01-21. Dirichlet's Lemma in Number Fields. https://arxiv.org/abs/2502.00526

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