Minimal vectors of pairs of dual lattices. (English) Zbl 0829.11036

Bergé, A.-M.

J. Number Theory 52, No. 2, 284-298 (1995).

The author classifies pairs of dual lattices in Euclidean \(E^n\) by their minimal vectors. This leads to a natural enlargement by duality of the usual notion of a perfect lattice, which the author calls a ‘perfect pair’. It is shown that in any given dimension there are only finitely many perfect pairs.

Reviewer: J.M.Wills (Siegen)

MSC:

11H31	Lattice packing and covering (number-theoretic aspects)
11H56	Automorphism groups of lattices
52C17	Packing and covering in \(n\) dimensions (aspects of discrete geometry)

Keywords:

perfect pair; pairs of dual lattices; minimal vectors; perfect lattice