Best simultaneous Diophantine approximations of some cubic algebraic numbers

DOI10.5802/jtnb.365zbMath1071.11043OpenAlexW1998199222MaRDI QIDQ558115

Nicolas Chevallier

Publication date: 30 June 2005

Published in: Journal de Théorie des Nombres de Bordeaux (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=JTNB_2002__14_2_403_0

zbMATH Keywords

continued fractionsJacobi-Perron algorithmreal cubic numberssimultaneous diophantine approximation

Mathematics Subject Classification ID

Continued fractions and generalizations (11J70) Graph theory (05C99) Simultaneous homogeneous approximation, linear forms (11J13) Symbolic dynamics (37B10) Automata sequences (11B85) Approximation to algebraic numbers (11J68)

Related Items (6)

Periodic karyon expansions of cubic irrationals in continued fractions ⋮ Periodic karyon expansions of algebraic units in multidimensional continued fractions ⋮ Karyon expansions of Pisot numbers in multidimensional continued fractions ⋮ Boundary of the Rauzy fractal sets in \(\mathbb {R} \times \mathbb {C}\) generated by \(P(x) = x^4 - x^3 - x^2 - x - 1\) ⋮ Coding of a translation of the two-dimensional torus ⋮ Approximations of Algebraic Irrationalities with Matrices

Cites Work

• Combinatorial, ergodic and arithmetic properties of the Tribonacci substitution
• Simultaneous asymptotic diophantine approximations to a basis of real cubic number field
• Simultaneous diophantine approximations and cubic irrationals
• The Jacobi-Perron algorithm its theory and application
• Nombres algébriques et substitutions
• Best Simultaneously Diophantine Approximations. I. Growth Rates of Best Approximation Denominators
• Meilleures approximations d'un élément du tore
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