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On completely multiplicative automatic sequences
Journal of Number Theory ( IF 0.6 ) Pub Date : 2020-08-01 , DOI: 10.1016/j.jnt.2019.12.015
Shuo Li

In this article we prove that all completely multiplicative automatic sequences $(a_n)_{n \in \mathbf{N}}$ defined on $\mathbf{C}$, vanishing or not, can be written in the form $a_n=b_n\chi_n$ where $(b_n)_{n \in \mathbf{N}}$ is an almost constant sequence, and $(\chi_n)_{n \in \mathbf{N}}$ is a Dirichlet character.

中文翻译:

关于完全乘法的自动序列

在本文中,我们证明了在 $\mathbf{C}$ 上定义的所有完全乘法自动序列 $(a_n)_{n \in \mathbf{N}}$,无论是否消失,都可以写成 $a_n= b_n\chi_n$ 其中 $(b_n)_{n \in \mathbf{N}}$ 是一个几乎恒定的序列,而 $(\chi_n)_{n \in \mathbf{N}}$ 是一个狄利克雷字符。
更新日期:2020-08-01
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