%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 }