Optimality and uniqueness of the Leech lattice among lattices

被引：68

作者：

Cohn, Henry ^{[1
]}

Kumar, Abhinav ^{[2
]}

机构：

[1] Microsoft Res, Redmond, WA 98052 USA

[2] Harvard Univ, Dept Math, Cambridge, MA 02138 USA

来源：

ANNALS OF MATHEMATICS | 2009年 / 170卷 / 03期

关键词：

POSITIVE QUADRATIC-FORMS; BOUNDS; SPHERE; CODES;

D O I：

10.4007/annals.2009.170.1003

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

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.

引用

页码：1003 / 1050

页数：48

共 31 条

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[2]

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[3]

[Anonymous], 1999, ENCY MATH APPL

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