Critical modular lattices in the Gaussian core model
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866914339026370560 |
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| author | Joharian, Arian Vallentin, Frank Zimmermannn, Marc Christian |
| author_facet | Joharian, Arian Vallentin, Frank Zimmermannn, Marc Christian |
| contents | We discuss the local analysis of Gaussian potential energy of modular lattices. We present examples of $2$-modular lattices -- such as the $16$-dimensional Barnes-Wall lattice -- and $3$-modular lattices -- such as the $12$-dimensional Coxeter-Todd lattice -- that are locally universally optimal among lattices (in the sense of Cohn and Kumar). We also provide other $2$- and $3$-modular lattices that are not locally universally optimal, or not even critical in the Gaussian core model. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_22895 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Critical modular lattices in the Gaussian core model Joharian, Arian Vallentin, Frank Zimmermannn, Marc Christian Metric Geometry Number Theory We discuss the local analysis of Gaussian potential energy of modular lattices. We present examples of $2$-modular lattices -- such as the $16$-dimensional Barnes-Wall lattice -- and $3$-modular lattices -- such as the $12$-dimensional Coxeter-Todd lattice -- that are locally universally optimal among lattices (in the sense of Cohn and Kumar). We also provide other $2$- and $3$-modular lattices that are not locally universally optimal, or not even critical in the Gaussian core model. |
| title | Critical modular lattices in the Gaussian core model |
| topic | Metric Geometry Number Theory |
| url | https://arxiv.org/abs/2503.22895 |