Far Eastern Mathematical Journal

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The average number of vertexes of Klein polyhedrons for integer lattices


A. A. Illarionov, D. Slinkin

2011, issue 1, Ñ. 48–55


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.

Keywords:
high dimension continued fraction, relative minimum, Klein polyhedron

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References

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