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On Voronoi's cylindric minima theorem

A. V. Ustinov

Institute for Applied Mathematics, Khabarovsk Division, Far-Eastern Branch of the Russian Academy of Sciences, Khabarovsk

Abstract: 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.

Key words: lattice, Voronoi algorithm.

UDC: 514.174.6

MSC: Primary 11H06; Secondary 11H55

Received: 10.08.2011