Optimality and uniqueness of the Leech lattice among lattices

Details Optimality and uniqueness of the Leech lattice among lattices Optimality and uniqueness of the Leech lattice among lattices

2004-03-16

arxiv.org/abs/math/0403263v2

Annals of Mathematics 170 (2009), 1003-1050

Mathematics

Metric Geometry

39 pages, to appear in Annals of Mathematics

Scientific paper

10.4007/annals.2009.170.1003

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.

Affiliated with

Also associated with

No associations

Rating

Optimality and uniqueness of the Leech lattice among lattices does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Optimality and uniqueness of the Leech lattice among lattices, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Optimality and uniqueness of the Leech lattice among lattices will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-574538