On a multidimensional generalization of Lagrange's theorem on continued fractions
- 26 February 2008
- journal article
- Published by Steklov Mathematical Institute in Izvestiya: Mathematics
- Vol. 72 (1), 47-61
- https://doi.org/10.1070/im2008v072n01abeh002391
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.This publication has 8 references indexed in Scilit:
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