On multidimensional generalization of the Lagrange theorem on continued fractions

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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.
13 pages, 15 references

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Number Theory, 11H06, 11H46, 11H50

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http://salesiana.dossiersoluciones.com/handle/123456789/169993

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0607084
 http://arxiv.org/abs/math/0607084

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arXiv