Algebraic Number Theory
《Algebraic Number Theory》 · 第 467–468 页 · Chapter VII，Section 5「The Dedekind Zeta Function」，Corollary 5.11 后
At $s=1$ it has a simple pole with residue $\operatorname{Res}_{s=1}\zeta_K(s)=\frac{2^{r_1}(2\pi)^{r_2}}{w|d_K|^{1/2}}hR$. […] The formula for the residue is commonly known as the analytic class number formula.