Year: 2014
Type: preprint
Abstract: We compare for an $n$-dimensional Euclidean lattice $\Lb$ the smallest possible values of the product of the norms of $n$~vectors which either constitute a basis for $\Lb$ (Hermite-type inequalities) or are merely assumed to be independent (Minkowski-type inequalities). We improve on 1953 results of van der Waerden in dimensions $6$ to $8$ and prove partial result in dimension~$9$.
Source: arXiv (Cornell University)
Author: Martinet, Jacques
Institution: Institut de Mathématiques de Bordeaux
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4300418134