Geodesic
The Dirchlet $L$-function does not vanish for $s=1$
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 2 (2015), pp. 57-59 
V. N. Chubarikov. The Dirchlet $L$-function does not vanish for $s=1$. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 2 (2015), pp. 57-59. http://geodesic.mathdoc.fr/item/VMUMM_2015_2_a11/
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     title = {The {Dirchlet} $L$-function does not vanish for $s=1$},
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Voir la notice de l'article provenant de la source Math-Net.Ru

A new proof of Dirichlet's theorem that a Dirichlet $L$-series for a prime modulo $q\equiv 3\pmod 4$ with a real character does not vanish is given.

[1] Davenport H., Multiplicative number theory, Graduate Texts in Mathematics, 74, 2nd ed., Springer-Verlag, N.Y.–Heidelberg–Berlin, 1980 | DOI | MR | Zbl

[2] Devenport G., Multiplikativnaya teoriya chisel, Nauka, M., 1971 | MR

[3] Arkhipov G.I., Sadovnichii V.A., Chubarikov V.N., Lektsii po matematicheskomu analizu, Drofa, M., 2008