Minkowski’s Conjecture, Well-rounded Lattices and Topological Dimension
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Counterexamples to a Conjecture of Woods
A conjecture of Woods from 1972 is disproved. A lattice in R is called well-rounded if its shortest nonzero vectors span R, is called unimodular if its covolume is equal to one, and the covering radius of a lattice Λ is the least r such that R = Λ + Br, where Br is the closed Euclidean ball of radius r. Let Nd denote the greatest value of the covering radius over all well-rounded unimodular lat...
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تاریخ انتشار 2005