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This article is cited in 6 scientific papers (total in 6 papers)
On the statistical properties of Klein polyhedra in three-dimensional lattices
A. A. Illarionov Institute for Applied Mathematics, Khabarovsk Division, Far-Eastern Branch of the Russian Academy of Sciences
Abstract:
We obtain asymptotic formulae for the average values of the number of faces of a fixed type and of vertices of Klein polyhedra of three-dimensional integer lattices with a given determinant.
Bibliography: 20 titles.
Keywords:
lattice, Klein polyhedron, multi-dimensional continued fraction, relative minimum.
Received: 01.12.2010 and 18.03.2013
Citation:
A. A. Illarionov, “On the statistical properties of Klein polyhedra in three-dimensional lattices”, Mat. Sb., 204:6 (2013), 23–46; Sb. Math., 204:6 (2013), 801–823
Linking options:
https://www.mathnet.ru/eng/sm7826https://doi.org/10.1070/SM2013v204n06ABEH004321 https://www.mathnet.ru/eng/sm/v204/i6/p23
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Abstract page: | 572 | Russian version PDF: | 171 | English version PDF: | 4 | References: | 72 | First page: | 53 |
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