Une forme dual-extrême irrationnelle

Abstract

This paper presents the five-dimensional lattices having an automorphism of order five from the point of view of duality. The first example of an irrational pair of polar lattices extreme with respect to the product of their Hermite constants arises in this set. The complete classification of the subset of isodual lattices enables us to give a partial answer to a question of Conway and Sloane.