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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2211.09044 |
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| _version_ | 1866914791869644800 |
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| author | de Courcy-Ireland, Matthew Dostert, Maria Viazovska, Maryna |
| author_facet | de Courcy-Ireland, Matthew Dostert, Maria Viazovska, Maryna |
| contents | We prove that the Cohn-Elkies linear programming bound for sphere packing is not sharp in dimension 6. The proof uses duality and optimization over a space of modular forms, generalizing a construction of Cohn-Triantafillou to the case of odd weight and non-trivial character. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_09044 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Six-dimensional sphere packing and linear programming de Courcy-Ireland, Matthew Dostert, Maria Viazovska, Maryna Metric Geometry Number Theory 52C17, 11F30, 11F25, 11Y99, 42A38, 49N15, 52C23 We prove that the Cohn-Elkies linear programming bound for sphere packing is not sharp in dimension 6. The proof uses duality and optimization over a space of modular forms, generalizing a construction of Cohn-Triantafillou to the case of odd weight and non-trivial character. |
| title | Six-dimensional sphere packing and linear programming |
| topic | Metric Geometry Number Theory 52C17, 11F30, 11F25, 11Y99, 42A38, 49N15, 52C23 |
| url | https://arxiv.org/abs/2211.09044 |