Henry Cohn, Abhinav Kumar, Stephen D. Miller, Danylo Radchenko, Maryna Viazovska
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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.
arXiv comments
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
Sphere packings are quite a deep and fascinating area of pure mathemaics. It has close relations to coding theory, lattice theory, number theory, modular forms. John Conway [1] (who recently passed away due to COVID) wrote a famous book about it: Sphere Packings, Lattices and…
Sphere packings are quite a deep and fascinating area of pure mathemaics. It has close relations to coding theory, lattice theory, number theory, modular forms. John Conway [1] (who recently passed away due to COVID) wrote a famous book about it: Sphere Packings, Lattices and…
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