On a multidimensional generalization of Lagrange's theorem on continued fractions

DOI10.1070/IM2008v072n01ABEH002391zbMath1180.11022arXivmath/0607084OpenAlexW2015365026MaRDI QIDQ3520099

Oleg N. German, Evgeny Lakshtanov

Publication date: 20 August 2008

Published in: Izvestiya: Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0607084

zbMATH Keywords

multidimensional continued fractionOppenheim conjectureKlein polyhedrasail

Mathematics Subject Classification ID

Lattices and convex bodies (number-theoretic aspects) (11H06) Minima of forms (11H50) Products of linear forms (11H46)

Related Items (14)

On Hermite’s problem, Jacobi–Perron type algorithms, and Dirichlet groups ⋮ Distribution of facets of higher-dimensional Klein polyhedra ⋮ Unnamed Item ⋮ A multidimensional generalization of Lagrange's theorem on continued fractions ⋮ Linear recurrence sequences and periodicity of multidimensional continued fractions ⋮ Badly approximable matrices and Diophantine exponents ⋮ Rational approximation of maximal commutative subgroups of \(\mathrm{GL}(n,\mathbb R){\mathrm{GL}(n,\mathbb{R})}\) ⋮ On the finiteness and periodicity of the 𝑝-adic Jacobi–Perron algorithm ⋮ A criterion for the integral equivalence of two generalized convex integer polyhedra ⋮ The statistical properties of 3D Klein polyhedra ⋮ Symmetries of a two-dimensional continued fraction ⋮ On $p$-adic multidimensional continued fractions ⋮ A two-dimensional continued fraction algorithm with Lagrange and Dirichlet properties ⋮ Interior Klein polyhedra

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