The sphere packing problem in dimension 24

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

Research output: Contribution to journalArticlepeer-review

82 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 languageEnglish (US)
Pages (from-to)1017-1033
Number of pages17
JournalAnnals of Mathematics
Volume185
Issue number3
DOIs
StatePublished - 2017

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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