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- Title
A multidimensional generalization of Lagrange's theorem on continued fractions.
- Authors
Bykovskaya, A.
- Abstract
A multidimensional geometric analog of Lagrange's theorem on continued fractions is proposed. The multidimensional generalization of the geometric interpretation of a continued fraction uses the notion of a Klein polyhedron, that is, the convex hull of the set of nonzero points in the lattice ℤ contained inside some n-dimensional simplicial cone with vertex at the origin. A criterion for the semiperiodicity of the boundary of a Klein polyhedron is obtained, and a statement about the nonempty intersection of the boundaries of the Klein polyhedra corresponding to a given simplicial cone and to a certain modification of this cone is proved.
- Subjects
LAGRANGE'S series; POLYHEDRA; CONTINUED fractions; PARTIAL fractions; EIGENVALUES
- Publication
Mathematical Notes, 2012, Vol 92, Issue 3/4, p312
- ISSN
0001-4346
- Publication type
Article
- DOI
10.1134/S0001434612090039