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.

17 pages. The auxiliary file appendix.txt has been updated since publication in several ways that still follow the general strategy of the appendix but correct some details. Comments in the file explain the changes, and the original file is preserved as appendix-original.txt for comparison

References in corpus (3)

• The sphere packing problem in dimension 8
• A conceptual breakthrough in sphere packing
• Some properties of optimal functions for sphere packing in dimensions 8 and 24

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