On the sum of degrees of digits occurring in continued fraction expansions of Laurent series
On the sum of degrees of digits occurring in continued fraction expansions of Laurent series
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DOI：
10.1017/s0305004104008163
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发表时间：
2005-01
影响因子：
0.8
通讯作者：
Jun Wu
中科院分区：
文献类型：
--
作者：
Jun Wu
贝斯科维奇考虑了与二进展开式中表示的实数位数之和相关的集合的豪斯多夫维数。在本文中，我们提供了形式洛朗级数领域的连续分数展开式的类比。我们还计算具有多项式或指数逼近阶数的洛朗级数集合的豪斯多夫维数。这种近似比几乎所有洛朗级数（相对于哈尔测度）收敛得更快。
Bescovitch considered the Hausdorff dimensions of sets related to the sum of digits of real numbers represented in the dyadic expansions. In this paper, we provide an analogy for continued fraction expansions over the field of formal Laurent series. We also calculate the Hausdorff dimensions of sets of Laurent series which have given polynomial or exponential approximation orders. Such approximations converge faster than those of almost all Laurent series (with respect to the Haar measure).