On multidimensional generalization of the Lagrange theorem on continued fractions

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dc.creatorGerman, Oleg N.
dc.creatorLakshtanov, Evgeniy L.
dc.date2006-07-04
dc.date2008-09-26
dc.date.accessioned2026-07-07T10:05:23Z
dc.date.available2026-07-07T10:05:23Z
dc.descriptionThe 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.
dc.description13 pages, 15 references
dc.identifierhttps://arxiv.org/abs/math/0607084
dc.identifierhttp://arxiv.org/abs/math/0607084
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/169993
dc.subjectNumber Theory
dc.subject11H06, 11H46, 11H50
dc.titleOn multidimensional generalization of the Lagrange theorem on continued fractions
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