Hermite versus Minkowski
Number Theory
2014-03-07 v1
Abstract
We compare for an -dimensional Euclidean lattice the smallest possible values of the product of the norms of ~vectors which either constitute a basis for (Hermite-type inequalities) or are merely assumed to be independent (Minkowski-type inequalities). We improve on 1953 results of van der Waerden in dimensions to and prove partial result in dimension~.
Cite
@article{arxiv.1403.1457,
title = {Hermite versus Minkowski},
author = {Jacques Martinet},
journal= {arXiv preprint arXiv:1403.1457},
year = {2014}
}