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| math.MG/0403263 |
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Title: Optimality and uniqueness of the Leech lattice among lattices
Authors: Henry Cohn, Abhinav Kumar
Categories: math.MG Metric Geometry
Comments: 39 pages
Abstract: We prove that the Leech lattice is the unique densest lattice in R^24. The
proof combines human reasoning with computer verification of the properties of
certain explicit polynomials. We furthermore prove that no sphere packing in
R^24 can exceed the Leech lattice's density by a factor of more than
1+1.65*10^(-30), and give a new proof that E_8 is the unique densest lattice in
R^8.
Owner: Henry Cohn
Version 1: Tue, 16 Mar 2004 13:57:38 GMT
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