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Proceedings of the American Mathematical Society
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
MathSciNet review: 0285499
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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.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1972-0285499-9
PII: S 0002-9939(1972)0285499-9
Keywords: Dirichlet $ L$-functions, primitive characters, functional equations
Article copyright: © Copyright 1972 American Mathematical Society