Mock characters and the Kronecker symbol

JOURNAL OF NUMBER THEORY

卷:192

Article

Allouche, Jean-Paul¹  Goldmakher, Leo² 

[1] Univ Paris 06, CNRS, Inst Math Jussieu PRG, Equipe Combinatoire & Optimisat, Case 247,4 Pl Jussieu, F-75252 Paris 05, France

[2] Williams Coll, Dept Math & Stat, Williamstown, MA 01267 USA

关键词: Completely multiplicative functions;    Automatic sequences;    Dirichlet characters;    Kronecker symbols;    Pretentiousness;   

DOI  :  10.1016/j.jnt.2018.04.022

来源: Elsevier

【 摘 要 】

We introduce and study a family of functions we call the mock characters. These functions satisfy a number of interesting properties, and of all completely multiplicative arithmetic functions seem to come as close as possible to being Dirichlet characters. Along the way we prove a few new results concerning the behaviour of the Kronecker symbol. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free