Geometry-of-numbers methods in the cusp
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2021
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| _version_ | 1866915293921542144 |
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| author | Shankar, Arul Siad, Artane Swaminathan, Ashvin Varma, Ila |
| author_facet | Shankar, Arul Siad, Artane Swaminathan, Ashvin Varma, Ila |
| contents | In this article, we develop new methods for counting integral orbits having bounded invariants that lie inside the cusps of fundamental domains for coregular representations. We illustrate these methods for a representation of cardinal interest in number theory, namely that of the split orthogonal group acting on the space of quadratic forms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2110_09466 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Geometry-of-numbers methods in the cusp Shankar, Arul Siad, Artane Swaminathan, Ashvin Varma, Ila Number Theory Representation Theory 11R29, 11R45, 11H55, 11P21, 11E76 In this article, we develop new methods for counting integral orbits having bounded invariants that lie inside the cusps of fundamental domains for coregular representations. We illustrate these methods for a representation of cardinal interest in number theory, namely that of the split orthogonal group acting on the space of quadratic forms. |
| title | Geometry-of-numbers methods in the cusp |
| topic | Number Theory Representation Theory 11R29, 11R45, 11H55, 11P21, 11E76 |
| url | https://arxiv.org/abs/2110.09466 |