Dirichlet's Lemma in Number Fields
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866917215549259776 |
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| author | Lemmermeyer, Franz |
| author_facet | Lemmermeyer, Franz |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_00526 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Dirichlet's Lemma in Number Fields Lemmermeyer, Franz Number Theory 11R29, 11R11 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. |
| title | Dirichlet's Lemma in Number Fields |
| topic | Number Theory 11R29, 11R11 |
| url | https://arxiv.org/abs/2502.00526 |