On simultaneous approximation to \((\alpha,\alpha^2)\) with \(\alpha^3+k\alpha-1=0\).

DOI10.1016/S0022-314X(02)00076-8zbMath1135.11326MaRDI QIDQ1874322

Shin-ichi Yasutomi, Shunji Ito, Hiroko Higashino, Junko Fujii

Publication date: 25 May 2003

Published in: Journal of Number Theory (Search for Journal in Brave)

zbMATH Keywords

simultaneous approximationbest simultaneous approximationmodified Jacobi-Perron algorithm

Mathematics Subject Classification ID

Continued fractions and generalizations (11J70) Simultaneous homogeneous approximation, linear forms (11J13)

Related Items (13)

Dynamical directions in numeration ⋮ 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 ⋮ Geometry, dynamics, and arithmetic of $S$-adic shifts ⋮ Levels of multi-continued fraction expansion of multi-formal Laurent series ⋮ Brun expansions of stepped surfaces ⋮ On optimal simultaneous rational approximation to \((\omega ,\omega ^{2})^{\tau}\) with \(\omega \) being some kind of cubic algebraic function ⋮ Parametrization of a two-dimensional quasiperiodic Rauzy tiling ⋮ A new multidimensional continued fraction algorithm ⋮ \(AH\)-substitution and Markov partition of a group automorphism on \(T^d\) ⋮ A combinatorial approach to products of Pisot substitutions ⋮ A New Multidimensional Slow Continued Fraction Algorithm and Stepped Surface

Cites Work

• Modified Jacobi-Perron algorithm and generating Markov partitions for special hyperbolic toral automorphisms
• Parallelogram tilings and Jacobi-Perron algorithm
• Simultaneous asymptotic diophantine approximations to a basis of real cubic number field
• On almost everywhere exponential convergence of the modified Jacobi-Perron algorithm: a corrected proof
• Unnamed Item

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