Generalized $(t,s)$-sequences, Kronecker-type sequences, and Diophantine approximations of formal Laurent series
Generalized $(t,s)$-sequences, Kronecker-type sequences, and Diophantine approximations of formal Laurent series
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形式洛朗级数的广义 $(t,s)$ 序列、Kronecker 型序列和丢番图近似
DOI：
10.1090/s0002-9947-1995-1290724-1
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发表时间：
1995
影响因子：
1.3
通讯作者：
H. Niederreiter
中科院分区：
文献类型：
--
作者：
G. Larcher;H. Niederreiter
（t, s）序列理论导致了在s维单位立方体中构造低差异序列的强大方法。我们推广了这一理论，以涵盖由数字方法构造的任意序列，特别是第二作者介绍的kronecker型序列。我们定义了有限域上形式Laurent级数的丢芬图近似常数，并证明了它们与kronecker型序列的分布性质的联系。主要结果包括数字方法构造的序列分布的概率定理和有限域上形式洛朗级数的s-元组的丢芬图近似性质。
The theory of (t, s)-sequences leads to powerful constructions of low-discrepancy sequences in an s-dimensional unit cube. We generalize this theory in order to cover arbitrary sequences constructed by the digital method and, in particular, the Kronecker-type sequences introduced by the second author. We define diophantine approximation constants for formal Laurent series over finite fields and show their connection with the distribution properties of Kronecker-type sequences. The main results include probabilistic theorems on the distribution of sequences constructed by the digital method and on the diophantine approximation character of s-tuples of formal Laurent series over finite fields.