Dirichlet’s Lemma in number fields
Acta Arithmetica
MSC: Primary 11R11; Secondary 11R29
DOI: 10.4064/aa250126-19-8
Published online: 28 October 2026
Abstract
Dirichlet’s Lemma states that every primitive quadratic Dirichlet character $\chi $ can be written in the form $\chi (n) = \big(\frac{\varDelta }n\big)$ for a suitable quadratic discriminant $\varDelta $. In this article we define a group, the separant class group $\mathrm{SCl}(F)$, that measures the extent to which Dirichlet’s Lemma fails in general number fields $F$.
