Dedekind zeta functions

Let $K$ be a number field (ie, a finite extension of the rationals $\mathbb Q$), with ring of integers ${{\mathcal O}_K}$. The Dedekind zeta function of $K$ is given by

\zeta_K(s)=\sum_{\mathfrak a} (N{\mathfrak a})^{-s} ,

for $\sigma>1$, where the sum is over all integral ideals of ${{\mathcal O}_K}$, and $N{\mathfrak a}$ is the norm of $\mathfrak a$.

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