ON THE LARGEST DEGREE OF THE PARTIAL QUOTIENTS IN CONTINUED FRACTION EXPANSIONS OVER THE FIELD OF FORMAL LAURENT SERIES
ON THE LARGEST DEGREE OF THE PARTIAL QUOTIENTS IN CONTINUED FRACTION EXPANSIONS OVER THE FIELD OF FORMAL LAURENT SERIES
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关于正式洛朗级数域上连分式展开的最大阶次商
DOI：
10.1142/s1793042113500231
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发表时间：
2013-08-01
影响因子：
0.7
通讯作者：
Jing, Huiping
中科院分区：
文献类型：
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作者：
Shen, Luming;Xu, Jian;Jing, Huiping
对于x是I的元素，设[A（1）（x），A（2）（x），... ]是洛朗级数域上的连分式展开式，记为L-n（x）：= max{deg A（1）（x），degA（2）（x），.，deg A（n）（x）}，这被称为最大程度的偏导数。本文给出了L-n（x）的一个重对数型定理，并由此得到对P-几乎所有x都是I的元素，lim（n ->+无穷大）L-n（x）/log（q）n = 1.并确定了相关例外集的Hausdorff维数。
For x is an element of I, let [A(1)(x), A(2)(x), ... ] be the continued fraction expansions over the field of Laurent series, write L-n(x) := max{deg A(1)(x), degA(2)(x), ... , deg A(n)(x)}, which is called the largest degree of partial quotients. In this paper, we give an iterated logarithm type theorem for L-n(x), and by which, we get that for P-almost all x is an element of I, lim(n ->+infinity) L-n(x)/log(q) n = 1. Also the Hausdorff dimensions of the related exceptional sets are determined.