Well-rounded algebraic lattices in odd prime dimension (Q1721759)

A lattice is a discrete additive subgroup of ${\mathbb R}^d$. It is well-rounded if it has a subset of $d$ linearly independent vectors of minimum norm. The authors give a construction of well-rounded lattices in Euclidean space of odd prime dimension. They show that for each abelian number field of odd prime degree having square-free conductor, there exists a ${\mathbb Z}$-module $M$, where the canonical embedding applied to the module produces a well-rounded lattice. Additionally, they show that for each odd prime dimension there are infinitely many non-equivalent well-rounded algebraic lattices.