论文标题
thue-morse序列的相关性
Correlations of the Thue--Morse sequence
论文作者
论文摘要
重新审视了Thue-Morse序列和系统的对相关性，重点介绍了各种均值的渐近结果。首先，结果表明，Thue-Morse序列具有一般实际权重的所有高阶相关性均由平衡$ 2 $ - 点相关的单个值有效地确定。结果，我们表明，平衡thue-morse序列的所有奇数相关都消失了，并且对于任何甚至$ n $，平衡thue thue-morse序列的$ n $ point的相关性的平均值零，其绝对值也提高到了任意正势。所有这些结果也适用于整个thue-morse系统。我们通过展示如何从平衡的$ 2 $ - 点相关性得出的thue-morse系统的相关性结束。
The pair correlations of the Thue--Morse sequence and system are revisited, with focus on asymptotic results on various means. First, it is shown that all higher-order correlations of the Thue--Morse sequence with general real weights are effectively determined by a single value of the balanced $2$-point correlation. As a consequence, we show that all odd-order correlations of the balanced Thue--Morse sequence vanish, and that, for any even $n$, the $n$-point correlations of the balanced Thue--Morse sequence have mean value zero, as do their absolute values, raised to an arbitrary positive power. All these results also apply to the entire Thue--Morse system. We finish by showing how the correlations of the Thue--Morse system with general real weights can be derived from the balanced $2$-point correlations.
