Quadratic fields: $\zeta_K(s)=\zeta(s)L(s,\chi)$, and the residue is $L(1,\chi)$ · Prove2Me

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Quadratic fields: $\zeta_K(s)=\zeta(s)L(s,\chi)$, and the residue is $L(1,\chi)$ · Prove2Me