Tempered Perfect Lattices in the Binary Case
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866913303071031296 |
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| author | Bahnson, Erik McConnell, Mark McIntosh, Kyrie |
| author_facet | Bahnson, Erik McConnell, Mark McIntosh, Kyrie |
| contents | A new algorithm for computing Hecke operators for SL(n,Z) was introduced by MacPherson, McConnell in 2020. The algorithm uses tempered perfect lattices, which are certain pairs of lattices together with a quadratic form. These generalize the perfect lattices of Voronoi. The present paper is the first step in characterizing tempered perfect lattices. We obtain a complete classification in the plane, where the Hecke operators are for SL(2,Z) and its arithmetic subgroups. The results depend on the class field theory of orders in imaginary quadratic number fields. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_10359 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Tempered Perfect Lattices in the Binary Case Bahnson, Erik McConnell, Mark McIntosh, Kyrie Number Theory 2020: 11F75 (primary), 11E16, 11F25, 11H55, 11R29 (secondary) A new algorithm for computing Hecke operators for SL(n,Z) was introduced by MacPherson, McConnell in 2020. The algorithm uses tempered perfect lattices, which are certain pairs of lattices together with a quadratic form. These generalize the perfect lattices of Voronoi. The present paper is the first step in characterizing tempered perfect lattices. We obtain a complete classification in the plane, where the Hecke operators are for SL(2,Z) and its arithmetic subgroups. The results depend on the class field theory of orders in imaginary quadratic number fields. |
| title | Tempered Perfect Lattices in the Binary Case |
| topic | Number Theory 2020: 11F75 (primary), 11E16, 11F25, 11H55, 11R29 (secondary) |
| url | https://arxiv.org/abs/2301.10359 |