Minimal Vectors of Pairs of Dual Lattices

✍ Scribed by A.M. Berge

• Publisher: Elsevier Science
• Year: 1995
• Tongue: English
• Weight: 555 KB
• Volume: 52
• Category: Article
• ISSN: 0022-314X
• DOI: 10.1006/jnth.1995.1071

✦ Synopsis

We classify (n)-dimensional pairs of dual lattices by their minimal vectors. This leads to the notion of a "perfect pair", a natural enlargement by duality of the usual notion of a perfect lattice, and we show that there are only finitely many of them in any given dimension. As an application, we obtain a finiteness theorem for pairs of dual lattices which are extremal with respect to the geometrical mean (\gamma^{\prime}) of their Hermite invariants. 1995 Academic Press, Inc.