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Lattices without short characteristic vectors

1998
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Mathematical Research Letters
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All the lattices here under discussion here are understood to be integral unimodular Z -lattices in R n . A characteristic vector of a lattice L is a vector w ∈ L such that v · w ≡ |v| 2 (mod 2) for every v ∈ L. Elkies has considered the minimal (squared) norm of the characteristic vectors in a unimodular lattice. He showed that any unimodular Z -lattice in R n has characteristic vectors of norm ≤ n; he also proved that of all such lattices, only the standard lattice Z n has no characteristic

doi:10.4310/mrl.1998.v5.n3.a8
fatcat:d3mximco2feahelgf5gkfhyfx4