1. Six-dimensional sphere packing and linear programming
- Author
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de Courcy-Ireland, Matthew, Dostert, Maria, and Viazovska, Maryna
- Subjects
Mathematics - Metric Geometry ,Mathematics - Number Theory ,52C17, 11F30, 11F25, 11Y99, 42A38, 49N15, 52C23 - Abstract
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., Comment: 36 pages, 3 figures, 3 tables, 3 supplementary text files; v3: corrected typos, simplified system (4.2) and equation (5.4); v4: same as v3 but more comments and two new formulas added to supplementary file
- Published
- 2022
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