On multidimensional generalization of the Lagrange theorem on continued fractions

Details On multidimensional generalization of the Lagrange theorem on continued fractions On multidimensional generalization of the Lagrange theorem on continued fractions

2006-07-04

arxiv.org/abs/math/0607084v3

Mathematics

Number Theory

13 pages, 15 references

Scientific paper

The Lagrange theorem on continued fractions states that a number is a quadratic surd if and only if its continued fraction expansion is eventually periodic. The current paper is devoted to a multidimensional generalization of this fact. As a multidimensional analog of continued fractions so called Klein polyhedra are considered: given an irrational lattice in an n-dimensional Euclidean space, its Klein polyhedron is defined as the convex hull of nonzero lattice points with nonnegative coordinates.

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