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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