On continued fractions and diophantine approximation in power series fields
On continued fractions and diophantine approximation in power series fields
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DOI：
10.4064/aa-95-2-139-166
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发表时间：
2000
期刊：
影响因子：
0.7
通讯作者：
W. Schmidt
中科院分区：
文献类型：
--
作者：
W. Schmidt
1.级数域中的连分数。虽然一些深入的工作已经做了连分数在幂级数领域，似乎没有一个一般性的介绍，或一个容易获得的帐户塞雷特定理或拉格朗日定理在这种情况下。因此，我们将从（显而易见的）定义开始，并设置一些符号。”[12]见。只要有可能，我们将尽量接近Perron的经典论文[19]中的方法。我们定义有理函数的变量Z 0，Z1，. . .通过（1）[Z 0] = Z 0，[Z 0，Z1] = Z 0 + 1/Z1，（1.1）[Z 0，Z1，. . .，Zn] = [Z0，. . .，Zn−2，Zn−1 + 1/Zn]（n ≥ 2）.（1.2）
1. Continued fractions in fields of series. While some deep work has been done on continued fractions in power series fields, there does not seem to exist a general introduction, or an easily accessible account of Serret’s Theorem or Lagrange’s Theorem in this case. We therefore will start with the (obvious) definitions, and set some notation. But see also [12]. Whenever possible, we will try to stay close to the approach in Perron’s classical treatise [19]. We define rational functions in variables Z0, Z1, . . . by (1) [Z0] = Z0, [Z0, Z1] = Z0 + 1/Z1, (1.1) [Z0, Z1, . . . , Zn] = [Z0, . . . , Zn−2, Zn−1 + 1/Zn] (n ≥ 2). (1.2)