Geometry & Topology, Vol. 6 (2002) Paper no. 10, pages 329--353.

New upper bounds on sphere packings II

Henry Cohn

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

AMS subject classification. Primary: 52C17, 52C07. Secondary: 33C10, 33C45.

DOI: 10.2140/gt.2002.6.329

E-print: arXiv:math.MG/0110010

Submitted to GT on 5 October 2001. Paper accepted 25 May 2002. Paper published 25 June 2002.

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Henry Cohn
Microsoft Research, One Microsoft Way
Redmond, WA 98052-6399, USA
Email: cohn@microsoft.com
URL: http://research.microsoft.com/~cohn
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