Hermite versus Minkowski
| Autor: | Martinet, Jacques |
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| Rok vydání: | 2014 |
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| Druh dokumentu: | Working Paper |
| Popis: | 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~$9$. |
| Databáze: | arXiv |
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