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On simultaneous rational approximation to \( (\alpha,\alpha^2)^{\text{T}}\) with \(\alpha^3+kd \alpha-d=0\). (Chinese. English summary) Zbl 1240.11074
Summary: The simultaneous rational approximation to \( (\alpha, \alpha^2)\) is studied by the modified Jacobi-Perrom algorithm (MJPA). It is proved that MJPA in the field of Laurent series gives the optimal simultaneous rational approximation to \( (\alpha, \alpha^2)\), where \(\alpha^3+kd \alpha-d=0,\;k,\;d\) are polynomials of positive degree over \(z\). This result is a generalization of S. Ito et al.’s result [J. Number Theory 99, No. 2, 255–283 (2003; Zbl 1135.11326)] in real number field.
MSC:
11J70 Continued fractions and generalizations
11J13 Simultaneous homogeneous approximation, linear forms
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