Most totally real fields do not have universal forms or Northcott property
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866912399699738624 |
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| author | Daans, Nicolas Kala, Vitezslav Man, Siu Hang Widmer, Martin Yatsyna, Pavlo |
| author_facet | Daans, Nicolas Kala, Vitezslav Man, Siu Hang Widmer, Martin Yatsyna, Pavlo |
| contents | We show that, in the space of all totally real fields equipped with the constructible topology, the set of fields that admit a universal quadratic form, or have the Northcott property, is meager. The main tool is a new theorem on the number of square classes of totally positive units represented by a quadratic lattice of a given rank. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_11082 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Most totally real fields do not have universal forms or Northcott property Daans, Nicolas Kala, Vitezslav Man, Siu Hang Widmer, Martin Yatsyna, Pavlo Number Theory 11E12, 11E20, 11G50, 11H55, 11R04, 11R20, 11R80 We show that, in the space of all totally real fields equipped with the constructible topology, the set of fields that admit a universal quadratic form, or have the Northcott property, is meager. The main tool is a new theorem on the number of square classes of totally positive units represented by a quadratic lattice of a given rank. |
| title | Most totally real fields do not have universal forms or Northcott property |
| topic | Number Theory 11E12, 11E20, 11G50, 11H55, 11R04, 11R20, 11R80 |
| url | https://arxiv.org/abs/2409.11082 |