On the index system of well-rounded lattices

2012/02/10 by Jacques Martinet, Martinet, Jacques
Computer Science · Mathematics · #Digital Image Processing Techniques #Mathematical Dynamics and Fractals #Point processes and geometric inequalities #math.NT #msc:11H55

paper · pdf · doi:10.48550/arxiv.1202.2295

17 pages

arxiv created 2012/02/10 · arxiv updated 2012/02/13

Abstract

Let \Lb be a lattice in an n-dimensional Euclidean space E and let \Lb' be a Minkowskian sublattice of \Lb, that is, a sublattice having a basis made of representatives for the Minkowski successive minima of \Lb. We consider the set of possible quotients \Lb/\Lb' which may exists in a given dimension or among not too large values of the index [\Lb:\Lb'], indeed [\Lb:\Lb']≤ 4, or dimension n≤ 8.

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