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 we give a new proof that E_8 is the unique densest lattice
in R^8.
Description
Optimality and uniqueness of the Leech lattice among lattices
%0 Generic
%1 cohn2004optimality
%A Cohn, Henry
%A Kumar, Abhinav
%D 2004
%K lattice lattices leech optimality uniqueness
%R 10.4007/annals.2009.170.1003
%T Optimality and uniqueness of the Leech lattice among lattices
%U http://arxiv.org/abs/math/0403263
%X 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 we give a new proof that E_8 is the unique densest lattice
in R^8.
@misc{cohn2004optimality,
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 we give a new proof that E_8 is the unique densest lattice
in R^8.},
added-at = {2013-12-23T05:16:30.000+0100},
author = {Cohn, Henry and Kumar, Abhinav},
biburl = {https://www.bibsonomy.org/bibtex/25f2b4fb6e399d08e7e5c9139581ada16/aeu_research},
description = {Optimality and uniqueness of the Leech lattice among lattices},
doi = {10.4007/annals.2009.170.1003},
interhash = {85c773e0d72085905c0d85f87efc3486},
intrahash = {5f2b4fb6e399d08e7e5c9139581ada16},
keywords = {lattice lattices leech optimality uniqueness},
note = {cite arxiv:math/0403263Comment: 39 pages, to appear in Annals of Mathematics},
timestamp = {2013-12-23T05:16:30.000+0100},
title = {Optimality and uniqueness of the Leech lattice among lattices},
url = {http://arxiv.org/abs/math/0403263},
year = 2004
}