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JOURNALS // Dal'nevostochnyi Matematicheskii Zhurnal // Archive

Dal'nevost. Mat. Zh., 2011 Volume 11, Number 1, Pages 48–55 (Mi dvmg210)

This article is cited in 6 papers

The average number of vertexes of Klein polyhedrons for integer lattices

A. A. Illarionov, D. Slinkin

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

Abstract: Low estimate for the average number for vertices of Klein polyhedron of integer lattices with given determinant is derived. The low estimate coincides with the high estimate up to a constant. The constant depends on dimension of lattices. High-low estimates for the number of relative minima of integer lattices with given determinant is derived from this fact.

Key words: high dimension continued fraction, relative minimum, Klein polyhedron.

UDC: 511.36, 511.9

MSC: Primary 11K60; Secondary 11G70

Received: 02.09.2010



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