Hermite versus Minkowski

Jacques Martinet

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arXiv · 1403.1457

Hermite versus Minkowski

Jacques Martinet

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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~$9$.

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Jacques Martinet. 2014-03-06. Hermite versus Minkowski. https://arxiv.org/abs/1403.1457

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