论文标题
沿Piatetski-Shapiro序列同步自动序列
Synchronizing automatic sequences along Piatetski-Shapiro sequences
论文作者
论文摘要
本文的目的是研究沿PIATETSKI-SHAPIRO序列$ \ lfloor n^c \ rfloor $与non-integer $ c> 1 $同步的$ k $ -automatic序列$ a（n）$。特别是，我们表明$ a（\ lfloor n^c \ rfloor）$满足$ \ sum_ {n \ le x}λ（n）a（\ lfloor n^c \ rfloor）\ sim c \ sim c \ sim c \ s $ c \ y crathers in crathertians的质量定理。 \ Mathbb z $。作为一个有趣的附加结果，我们表明序列$ \ lfloor n^c \ rfloor \ bmod m $具有多项式子单词复杂性。
The purpose of this paper is to study subsequences of synchronizing $k$-automatic sequences $a(n)$ along Piatetski-Shapiro sequences $\lfloor n^c \rfloor$ with non-integer $c>1$. In particular, we show that $a(\lfloor n^c \rfloor)$ satisfies a prime number theorem of the form $\sum_{n\le x} Λ(n)a(\lfloor n^c \rfloor) \sim C\, x$, and, furthermore, that it is deterministic for $c \in \mathbb R\setminus \mathbb Z$. As an interesting additional result, we show that the sequence $\lfloor n^c\rfloor \bmod m$ has polynomial subword complexity.
