Geodesic
On Voronoi's cylindric minima theorem
Dalʹnevostočnyj matematičeskij žurnal, Tome 11 (2011) no. 2, pp. 213-221.

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Voronoi's algorithm for computing a system of fundamental units of a complex number field is based on a geometric properties of 3-dimensional lattices. This algorithm is based on Voronoi's theorem about cylindric minima for a lattice in general position. In the original proof and it's refinement published by Delone and Faddeev some significant cases were skipped. In the present we give a complete proof of Voronoi's theorem. The result is extended to arbitrary lattices. 
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A. V. Ustinov. On Voronoi's cylindric minima theorem. Dalʹnevostočnyj matematičeskij žurnal, Tome 11 (2011) no. 2, pp. 213-221. http://geodesic.mathdoc.fr/item/DVMG_2011_11_2_a7/

[1] G. Voronoi, Ob odnom obobschenii algorifma nepreryvnykh drobei, Tipografiya Varshavskogo Uchebnogo Okruga, Varshava, 1896

[2] B. N. Delone, D. K. Faddeev, Teoriya irratsionalnostei tretei stepeni, izd-vo AN SSSR, M.–L., 1940

[3] B. N. Delone, Peterburgskaya shkola teorii chisel, izd-vo AN SSSR, M.–L., 1947

[4] A. A. Illarionov, “O tsilindricheskikh minimumakh trekhmernykh reshetok”, Dalnevost. matem. zhurn., 11:1 (2011), 48–55 | Zbl