Number fields with prescribed norms
Fuente:
arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2018
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866917642046013440 |
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| author | Frei, Christopher Loughran, Daniel Newton, Rachel Harpaz, Yonatan Wittenberg, Olivier |
| author_facet | Frei, Christopher Loughran, Daniel Newton, Rachel Harpaz, Yonatan Wittenberg, Olivier |
| contents | We study the distribution of extensions of a number field $k$ with fixed abelian Galois group $G$, from which a given finite set of elements of $k$ are norms. In particular, we show the existence of such extensions. Along the way, we show that the Hasse norm principle holds for $100\%$ of $G$-extensions of $k$, when ordered by conductor. The appendix contains an alternative purely geometric proof of our existence result. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1810_06024 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | Number fields with prescribed norms Frei, Christopher Loughran, Daniel Newton, Rachel Harpaz, Yonatan Wittenberg, Olivier Number Theory 11R37 (primary), 11R45, 43A70, 14G05, 20G30 (secondary) We study the distribution of extensions of a number field $k$ with fixed abelian Galois group $G$, from which a given finite set of elements of $k$ are norms. In particular, we show the existence of such extensions. Along the way, we show that the Hasse norm principle holds for $100\%$ of $G$-extensions of $k$, when ordered by conductor. The appendix contains an alternative purely geometric proof of our existence result. |
| title | Number fields with prescribed norms |
| topic | Number Theory 11R37 (primary), 11R45, 43A70, 14G05, 20G30 (secondary) |
| url | https://arxiv.org/abs/1810.06024 |