Geodesic
A note on Linnik's approach to the Dirichlet $L$-functions
Informatics and Automation, Analytic and combinatorial number theory, Tome 296 (2017), pp. 123-132.

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Let $\chi \pmod q$, $q>1$, be a primitive Dirichlet character. We first present a detailed account of Linnik's deduction of the functional equation of $L(s,\chi )$ from the functional equation of $\zeta (s)$. Then we show that the opposite deduction can be obtained by a suitable modification of the method, involving finer arithmetic arguments. 
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J. Kaczorowski; A. Perelli. A note on Linnik's approach to the Dirichlet $L$-functions. Informatics and Automation, Analytic and combinatorial number theory, Tome 296 (2017), pp. 123-132. http://geodesic.mathdoc.fr/item/TRSPY_2017_296_a8/

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