Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Dirichlet $ L$-functions and primitive characters


Author: Tom M. Apostol
Journal: Proc. Amer. Math. Soc. 31 (1972), 384-386
DOI: https://doi.org/10.1090/S0002-9939-1972-0285499-9
MathSciNet review: 0285499
Full-text PDF Free Access

Abstract | References | Additional Information

Abstract: It is well known that a Dirichlet $ L$-function $ L(s,\chi )$ has a functional equation if the character $ \chi $ is primitive. This note proves the converse result. That is, if $ L(s,\chi )$ satisfies the usual functional equation then $ \chi $ is primitive.


References [Enhancements On Off] (What's this?)


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1972-0285499-9
Keywords: Dirichlet $ L$-functions, primitive characters, functional equations
Article copyright: © Copyright 1972 American Mathematical Society