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On multidimensional generalization of the Lagrange theorem on continued fractions

Oleg N. German·Evgeniy L. Lakshtanov
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Abstract

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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Oleg N. German, Evgeniy L. Lakshtanov. 2008-09-26. On multidimensional generalization of the Lagrange theorem on continued fractions. https://arxiv.org/abs/math/0607084

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