The sphere packing problem in dimension 24

被引：155

作者：

Cohn, Henry ^{[1
]}

Kumar, Abhinav ^{[2
]}

Miller, Stephen D. ^{[3
]}

Radchenko, Danylo ^{[4
,5
]}

Viazovska, Maryna ^{[6
,7
,8
]}

机构：

[1] Microsoft Res New England, Cambridge, MA 02142 USA

[2] SUNY Stony Brook, Stony Brook, NY 11794 USA

[3] Rutgers State Univ, Piscataway, NJ USA

[4] Max Planck Inst Math, Bonn, Germany

[5] Abdus Salam Int Ctr Theoret Phys, Trieste, Italy

[6] Berlin Math Sch, Berlin, Germany

[7] Humboldt Univ, Berlin, Germany

[8] Ecole Polytech Fed Lausanne, Lausanne, Switzerland

来源：

ANNALS OF MATHEMATICS | 2017年 / 185卷 / 03期

基金：

美国国家科学基金会;

关键词：

D O I：

10.4007/annals.2017.185.3.8

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

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.

引用

页码：1017 / 1033

页数：17

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