A note on multiplicative automatic sequences

被引：6

作者：

Klurman, Oleksiy ^{[1
]}

Kurlberg, Par ^{[1
]}

机构：

[1] KTH Royal Inst Technol, Dept Math, Stockholm, Sweden

来源：

COMPTES RENDUS MATHEMATIQUE | 2019年 / 357卷 / 10期

基金：

瑞典研究理事会;

关键词：

D O I：

10.1016/j.crma.2019.10.002

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove that any q-automatic completely multiplicative function f: N -> C essentially coincides with a Dirichlet character. This answers a question of J.-P. Allouche and L. Gold-makher and confirms a conjecture of J. Bell, N. Bruin and M. Coons for completely multiplicative functions. Further, assuming GRH, the methods allow us to replace completely multiplicative functions with multiplicative functions. (C) 2019 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.

引用

页码：752 / 755

页数：4

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