English

Hermite versus Minkowski

Number Theory 2014-03-07 v1

Abstract

We compare for an nn-dimensional Euclidean lattice \Lb\Lb the smallest possible values of the product of the norms of nn~vectors which either constitute a basis for \Lb\Lb (Hermite-type inequalities) or are merely assumed to be independent (Minkowski-type inequalities). We improve on 1953 results of van der Waerden in dimensions 66 to 88 and prove partial result in dimension~99.

Cite

@article{arxiv.1403.1457,
  title  = {Hermite versus Minkowski},
  author = {Jacques Martinet},
  journal= {arXiv preprint arXiv:1403.1457},
  year   = {2014}
}
R2 v1 2026-06-22T03:21:37.181Z