The sphere packing problem in dimension $24$ 论文
2017Annals of Mathematics引用 291
Mathematical Approximation and IntegrationDigital Image Processing TechniquesPoint processes and geometric inequalities
详细信息
- 发表期刊/会议
- Annals of Mathematics
- 发表日期
- 2017-02-24
- 发表年份
- 2017
关键词
Mathematical Approximation and IntegrationDigital Image Processing TechniquesPoint processes and geometric inequalities
摘要
Building on Viazovska's recent solution of the sphere packing problem in eight dimensions, we prove that the Leech lattice is the densest packing of congruent spheres in twenty-four dimensions and that it is the unique optimal periodic packing. In particular, we find an optimal auxiliary function for the linear programming bounds, which is an analogue of Viazovska's function for the eight-dimensional case.