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Dal'nevost. Mat. Zh., 2011, Volume 11, Number 2, Pages 213–221 (Mi dvmg223)  

This article is cited in 1 scientific paper (total in 1 paper)

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.

Full text: PDF file (291 kB)
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UDC: 514.174.6
MSC: Primary 11H06; Secondary 11H55
Received: 10.08.2011

Citation: A. V. Ustinov, “On Voronoi's cylindric minima theorem”, Dal'nevost. Mat. Zh., 11:2 (2011), 213–221

Citation in format AMSBIB
\Bibitem{Ust11}
\by A.~V.~Ustinov
\paper On Voronoi's cylindric minima theorem
\jour Dal'nevost. Mat. Zh.
\yr 2011
\vol 11
\issue 2
\pages 213--221
\mathnet{http://mi.mathnet.ru/dvmg223}


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    This publication is cited in the following articles:
    1. A. A. Illarionov, “On the average number of best approximations of linear forms”, Izv. Math., 78:2 (2014), 268–292  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
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