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 twentyfour 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 eightdimensional case.
 Publication:

arXiv eprints
 Pub Date:
 March 2016
 arXiv:
 arXiv:1603.06518
 Bibcode:
 2016arXiv160306518C
 Keywords:

 Mathematics  Number Theory;
 Mathematics  Metric Geometry
 EPrint:
 17 pages