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New upper bounds on sphere packings II

Henry Cohn

Geometry & Topology 6 (2002) 329–353

DOI: 10.2140/gt.2002.6.329

arXiv: math.MG/0110010
Abstract

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

Primary: 52C07, 52C17

Secondary: 33C10, 33C45
References
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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/