New upper bounds on sphere packings II

We continue the study of the linear programming bounds for sphere packing introduced by Cohn and Elkies. We use theta series to give another proof of the principal theorem, and present some related results and conjectures.

Keywords

sphere packing, linear programming bounds, lattice, theta series, Laguerre polynomial, Bessel function

Mathematical Subject Classification 2000

Primary: 52C17, 52C07

Secondary: 33C10, 33C45

References

Forward citations

Publication

Received: 5 October 2001

Accepted: 25 May 2002

Published: 25 June 2002

Proposed: Robion Kirby

Seconded: Michael Freedman, Walter Neumann

Authors

Henry Cohn
Microsoft Research One Microsoft Way Redmond Washington 98052-6399 USA
http://research.microsoft.com/~cohn/

Volume 6, issue 1 (2002)

Henry Cohn