Successive Minima, Determinant and Automorphism Groups of Hyperelliptic Function Field Lattices
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866929574681509888 |
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| author | Menn, Lilian Sacikara, Elif |
| author_facet | Menn, Lilian Sacikara, Elif |
| contents | In this paper, we contribute to previously known results on lattices constructed by algebraic function fields, or function field lattices in short. First, motivated by the non-well-roundedness property of certain hyperelliptic function field lattices (Ates and Stichtenoth, 2016), we explore the successive minima of these lattices in detail. We also study the determinant of hyperelliptic function field lattices. Finally, we show a connection between the automorphism groups of algebraic function fields and function field lattices, based on ideas from Böttcher et al., 2016. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_01559 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Successive Minima, Determinant and Automorphism Groups of Hyperelliptic Function Field Lattices Menn, Lilian Sacikara, Elif Number Theory In this paper, we contribute to previously known results on lattices constructed by algebraic function fields, or function field lattices in short. First, motivated by the non-well-roundedness property of certain hyperelliptic function field lattices (Ates and Stichtenoth, 2016), we explore the successive minima of these lattices in detail. We also study the determinant of hyperelliptic function field lattices. Finally, we show a connection between the automorphism groups of algebraic function fields and function field lattices, based on ideas from Böttcher et al., 2016. |
| title | Successive Minima, Determinant and Automorphism Groups of Hyperelliptic Function Field Lattices |
| topic | Number Theory |
| url | https://arxiv.org/abs/2411.01559 |