P. Lertchoosakul, A. Haddley, R. Nair, Michel J. G. Weber
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引用次数: 0
摘要
对于整数b > 1，设(φb(n))n≥0表示[0,1]中b中的van der Corput序列基。回答O. Strauch, C. aisstleitner和M. Hofer的问题，证明了(φb(n)， φb(n + 1)，…， φb(n + s−1))n≥0在[0,1)s上存在，并且是一个共轭。本文的第一和第三作者证明了这种现象可以扩展到van der Corput序列的一大类子序列。在这个结果中，我们进一步扩展了这篇论文，并表明这种现象也适用于基于W. Parry和A. r尼的β展开的更一般的计数系统。
Distribution Functions for Subsequences of Generalized Van Der Corput Sequences
Abstract For an integer b > 1 let (φb(n))n≥0 denote the van der Corput sequence base in b in [0, 1). Answering a question of O. Strauch, C. Aistleitner and M. Hofer showed that the distribution function of (φb(n), φb(n + 1), . . . , φb(n + s − 1))n≥0 on [0, 1)s exists and is a copula. The first and third authors of the present paper showed that this phenomenon extends to a broad class of subsequences of the van der Corput sequence. In this result we extend this paper still further and show that this phenomenon is also true for more general numeration systems based on the beta expansion of W. Parry and A. Rényi.
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