Hermite versus Minkowski

2014/03/06 by Martinet, Jacques
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1403.1457

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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