The sphere packing problem in dimension 24 on JSTOR

Annals of Mathematics

Description:

Annals of Mathematics, a distinguished journal of research papers in pure mathematics, was founded in 1884. Annals of Mathematics is published bimonthly with the cooperation of Princeton University and the Institute for Advanced Study. It is widely regarded as one of the main mathematics journals in the world.

Coverage: 1884-2020 (Vol. 1, No. 1 - Vol. 191, No. 1)

Moving Wall: 5 years (What is the moving wall?)

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ISSN: 0003486X

EISSN: 19398980

Subjects: Mathematics, Science & Mathematics

Collections: Arts & Sciences I Collection, JSTOR Archival Journal & Primary Source Collection, JSTOR Essential Collection, Mathematics & Statistics Collection

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.

The sphere packing problem in dimension 24

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Abstract