Dedekind zeta function

《Algebraic Number Theory》 · 第 321 页 · Section 9.3「Quadratic characters」

Let $K$ be an algebraic number field. The Dedekind zeta function of $K$ is defined to be $\zeta_K(s)=\sum_{\mathfrak a}N(\mathfrak a)^{-s}$ for $\sigma>1$, where the sum is over all integral ideals in the ring $\mathcal O_K$ of algebraic integers in $K$.