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math.NT2024
Families of Equiangular Lines and Lattices
Jacques Martinet
We construct Euclidean lattices whose sets of minimal vectors support some large equiangular families of lines, using notably reduction modulo~ of lattices. %as considered in \c…
math.NT2014
Hermite versus Minkowski
Jacques Martinet
We compare for an -dimensional Euclidean lattice $\Lb$ the smallest possible values of the product of the norms of ~vectors which either constitute a basis for $\Lb$ (Hermite…
math.NT2012
On the index system of well-rounded lattices
Jacques Martinet
Let $\Lb$ be a lattice in an -dimensional Euclidean space and let $\Lb'$ be a Minkowskian sublattice of $\Lb$, that is, a sublattice having a basis made of representatives f…