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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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Table of 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.