Optimality and uniqueness of the Leech lattice among lattices

• 成果类型: Article
• 署名作者: Cohn, Henry; Kumar, Abhinav
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2009.170.1003
• 发表日期: 2009
• 页码: 1003-1050
• 关键词: positive quadratic-forms; bounds; sphere; CODES

摘要

We prove that the Leech lattice is the unique densest lattice in R-24. The proof combines human reasoning with computer verification of the properties of certain explicit polynomials. We furthermore prove that no sphere packing in R-24 can exceed the Leech lattice's density by a factor of more than 1 + 1.65 . 10(-30), and we give a new proof that E-8 is the unique densest lattice in R-8.