Dirichlet $L$-functions and primitive characters
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- by Tom M. Apostol
- Proc. Amer. Math. Soc. 31 (1972), 384-386
- DOI: https://doi.org/10.1090/S0002-9939-1972-0285499-9
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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.References
- Tom M. Apostol, Dirichlet $L$-functions and character power sums, J. Number Theory 2 (1970), 223–234. MR 258766, DOI 10.1016/0022-314X(70)90022-3
- Tom M. Apostol, Euler’s $\phi$-function and separable Gauss sums, Proc. Amer. Math. Soc. 24 (1970), 482–485. MR 257006, DOI 10.1090/S0002-9939-1970-0257006-6
Bibliographic Information
- © Copyright 1972 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 31 (1972), 384-386
- DOI: https://doi.org/10.1090/S0002-9939-1972-0285499-9
- MathSciNet review: 0285499