On the Extremality of an 80-Dimensional Lattice

13 years 9 months ago
On the Extremality of an 80-Dimensional Lattice
Abstract. We show that a specific even unimodular lattice of dimension 80, first investigated by Schulze-Pillot and others, is extremal (i.e., the minimal nonzero norm is 8). This is the third known extremal lattice in this dimension. The known part of its automorphism group is isomorphic to SL2(F79), which is smaller (in cardinality) than the two previous examples. The technique to show extremality involves using the positivity of the Θ-series, along with fast vector enumeration techniques including pruning, while also using the automorphisms of the lattice.
Damien Stehlé, Mark Watkins
Added 15 Aug 2010
Updated 15 Aug 2010
Type Conference
Year 2010
Where ANTS
Authors Damien Stehlé, Mark Watkins
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