Geometry-of-numbers methods over global fields I: Prehomogeneous vector spaces
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2015
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| _version_ | 1866912962024833024 |
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| author | Bhargava, Manjul Shankar, Arul Wang, Xiaoheng |
| author_facet | Bhargava, Manjul Shankar, Arul Wang, Xiaoheng |
| contents | We develop geometry-of-numbers methods to count orbits in prehomogeneous vector spaces having bounded invariants over any global field. As our primary example, we apply these techniques to determine, for any base global field $F$, the density of discriminants of field extensions of degree at most 5 over $F$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1512_03035 |
| institution | arXiv |
| publishDate | 2015 |
| record_format | arxiv |
| spellingShingle | Geometry-of-numbers methods over global fields I: Prehomogeneous vector spaces Bhargava, Manjul Shankar, Arul Wang, Xiaoheng Number Theory 11R29, 11R45 We develop geometry-of-numbers methods to count orbits in prehomogeneous vector spaces having bounded invariants over any global field. As our primary example, we apply these techniques to determine, for any base global field $F$, the density of discriminants of field extensions of degree at most 5 over $F$. |
| title | Geometry-of-numbers methods over global fields I: Prehomogeneous vector spaces |
| topic | Number Theory 11R29, 11R45 |
| url | https://arxiv.org/abs/1512.03035 |