Six-dimensional sphere packing and linear programming
Metric Geometry
2024-05-14 v4 Number Theory
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.
Cite
@article{arxiv.2211.09044,
title = {Six-dimensional sphere packing and linear programming},
author = {Matthew de Courcy-Ireland and Maria Dostert and Maryna Viazovska},
journal= {arXiv preprint arXiv:2211.09044},
year = {2024}
}
Comments
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