Minimal rank of universal lattices and number of indecomposable elements in real multiquadratic fields
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arXiv
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866929336645320704 |
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| author | Man, Siu Hang |
| author_facet | Man, Siu Hang |
| contents | We establish an upper bound on the number of real multiquadratic fields that admit a universal quadratic lattice of a given rank, or contain a given amount of indecomposable elements modulo totally positive units, obtaining density zero statements. We also study the structure of indecomposable elements in real biquadratic fields, and compute a system of indecomposable elements modulo totally positive units for some families of real biquadratic fields. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_04908 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Minimal rank of universal lattices and number of indecomposable elements in real multiquadratic fields Man, Siu Hang Number Theory We establish an upper bound on the number of real multiquadratic fields that admit a universal quadratic lattice of a given rank, or contain a given amount of indecomposable elements modulo totally positive units, obtaining density zero statements. We also study the structure of indecomposable elements in real biquadratic fields, and compute a system of indecomposable elements modulo totally positive units for some families of real biquadratic fields. |
| title | Minimal rank of universal lattices and number of indecomposable elements in real multiquadratic fields |
| topic | Number Theory |
| url | https://arxiv.org/abs/2307.04908 |