Geodesic
On a problem in the geometry of numbers
Trudy Instituta matematiki, Tome 15 (2007) no. 1, pp. 111-117

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In this paper, a problem of the geometry of numbers is considered. The notion of the defect is introduced, which helps to measure the difference between a basis in a lattice and a basis in its centering. Various estimates for the defect are obtained as well as some new problems are discussed. 
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A. M. Raigorodskii. On a problem in the geometry of numbers. Trudy Instituta matematiki, Tome 15 (2007) no. 1, pp. 111-117. http://geodesic.mathdoc.fr/item/TIMB_2007_15_1_a12/