Abstract
Let F s = Q(α) be a real algebraic number field of degree s. We shall give in this chapter an algorithm for the simultaneous Diophantine approximation obtained by η l = αl (l = 1, 2, ....) which is essentially the Jacobi-Perron algorithm (Cf. L. Bernstein [1]). It yields less precise results but the computations of nl and h lj .(1 ≤ j ≤ s) are comparatively simple.
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Notes
The definition of PV number was first introduced by C. PisotDJ and T. Vijayaraghavan [1] (Cf. J. W. S. Cassels [1]).
Lemma 2.8: Cf. Hua Loo Keng [1].
Theorem 2.4 is due to Xie Ting Fan and Pei Ding Yi [1] which improves a theorem of O. Perron [1] and also a theorem of L. Bernstein [1].
The other results: Cf. Hua Loo Keng and Wang Yuan [6,7,8].
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© 1981 Springer-Verlag Berlin Heidelberg and Science Press. Beijing
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Keng, H.L., Yuan, W. (1981). Recurrence Relations and Rational Approximation. In: Applications of Number Theory to Numerical Analysis. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-67829-5_2
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DOI: https://doi.org/10.1007/978-3-642-67829-5_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-67831-8
Online ISBN: 978-3-642-67829-5
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