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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2509.04591 |
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| _version_ | 1866908519926595584 |
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| author | Santos, L. F. Jorge, G. C. |
| author_facet | Santos, L. F. Jorge, G. C. |
| contents | The lattices $D_4$ and $E_8$ are known to be the densest lattices in dimensions 4 and 8, respectively. In this paper, we employ tools from algebraic number theory to prove that the $D_4$-lattice arises from an infinite family of totally imaginary biquadratic fields. Furthermore, we extend this construction to show that both the $D_8$ and $E_8$ can be realized via triquadratic fields derived from this family. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_04591 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Constructions of lattices via biquadratic and triquadratic fields Santos, L. F. Jorge, G. C. Number Theory 11H06, 11H31, 11R11, 11R16 The lattices $D_4$ and $E_8$ are known to be the densest lattices in dimensions 4 and 8, respectively. In this paper, we employ tools from algebraic number theory to prove that the $D_4$-lattice arises from an infinite family of totally imaginary biquadratic fields. Furthermore, we extend this construction to show that both the $D_8$ and $E_8$ can be realized via triquadratic fields derived from this family. |
| title | Constructions of lattices via biquadratic and triquadratic fields |
| topic | Number Theory 11H06, 11H31, 11R11, 11R16 |
| url | https://arxiv.org/abs/2509.04591 |