The sphere packing problem in dimension 24

Henry Cohn; Abhinav Kumar; Stephen D. Miller; Danylo Radchenko; Maryna Viazovska

doi:10.4007/annals.2017.185.3.8

The sphere packing problem in dimension 24

Henry Cohn, Abhinav Kumar, Stephen D. Miller, Danylo Radchenko, Maryna Viazovska

School of Arts and Sciences, Mathematics

Research output: Contribution to journal › Article › peer-review

101 Scopus citations

Abstract

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.

Original language	English (US)
Pages (from-to)	1017-1033
Number of pages	17
Journal	Annals of Mathematics
Volume	185
Issue number	3
DOIs	https://doi.org/10.4007/annals.2017.185.3.8
State	Published - 2017

All Science Journal Classification (ASJC) codes

Statistics and Probability
Statistics, Probability and Uncertainty

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10.4007/annals.2017.185.3.8

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title = "The sphere packing problem in dimension 24",

abstract = "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.",

author = "Henry Cohn and Abhinav Kumar and Miller, {Stephen D.} and Danylo Radchenko and Maryna Viazovska",

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AU - Radchenko, Danylo

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N2 - 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.

AB - 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.

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The sphere packing problem in dimension 24

Abstract

All Science Journal Classification (ASJC) codes

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