On the index system of well-rounded lattices

Jacques Martinet (1)

1 IMB - Institut de Mathématiques de Bordeaux

Let $\Lb$ be a lattice in an $n$-dimensional Euclidean space $E$ and let $\Lb'$ be a Minkowskian sublattice of $\Lb$, that is, a sublattice having a basis made of representatives for the Minkowski successive minima of $\Lb$. We consider the set of possible quotients $\Lb/\Lb'$ which may exists in a given dimension or among not too large values of the index $[\Lb:\Lb']$, indeed $[\Lb:\Lb']\le 4$, or dimension $n\le 8$.

Domaines: Théorie des nombres [math.NT]

Jacques Martinet. On the index system of well-rounded lattices. 2012. ⟨hal-00956656⟩