Constructing multidimensional periodic continued fractions in the sense of Klein

DOI10.1090/S0025-5718-08-02187-XzbMath1215.11069arXivmath/0411031OpenAlexW2030887411MaRDI QIDQ3055166

Oleg N. Karpenkov

Publication date: 7 November 2010

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0411031

zbMATH Keywords

convex polygonsinteger latticesmultidimensional continued fractions

Mathematics Subject Classification ID

Lattices and convex bodies (number-theoretic aspects) (11H06) Continued fractions and generalizations (11J70) Continued fractions (11A55)

Related Items (8)

On Hermite’s problem, Jacobi–Perron type algorithms, and Dirichlet groups ⋮ Distribution of facets of higher-dimensional Klein polyhedra ⋮ Linear recurrence sequences and periodicity of multidimensional continued fractions ⋮ 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 ⋮ The statistical properties of 3D Klein polyhedra ⋮ On $p$-adic multidimensional continued fractions ⋮ On the periodic writing of cubic irrationals and a generalization of Rédei functions

Cites Work

• Higher dimensional analogues of periodic continued fractions and cusp singularities
• Factoring polynomials with rational coefficients
• Minima of decomposable forms of degree \(n\), in \(n\) variables for \(n\geq{} 3\)
• On the resolution of cusp singularities and the Shintani decomposition in totally real cubic number fields
• Higher dimensional continued fractions
• On an effective determination of a Shintani's decomposition of the cone \({\mathbb{R}}_ +^ n\)
• The simplest 2-dimensional continued fraction
• Sails and Hilbert bases
• Klein polyhedra for the fourth extremal cubic form
• Klein polyhedrals for two cubic Davenport forms
• On tori triangulations associated with two-dimensional continued fractions of cubic irrationalities
• Two-dimensional continued fractions of hyperbolic integer matrices with small norm
• Classification of three-dimensional multistorey completely empty convex marked pyramids
• Sails and norm minima of lattices
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Constructing multidimensional periodic continued fractions in the sense of Klein