For $\operatorname{Re}s>1$, the <Dedekind zeta function> of $K$ is
$$
\zeta_K(s)=\sum_{0\ne\mathfrak a\subseteq\mathcal O_K}(N\mathfrak a)^{-s}.
$$
Unique factorization of ideals gives its <Euler product>
$$
\zeta_K(s)=\prod_{\mathfrak p}\left(1-(N\mathfrak p)^{-s}\right)^{-1},
$$
over the nonzero prime ideals of $\mathcal O_K$.

Solution

Past exam of the mathematics course of the University of Cambridge / 2023 / iii / Paper 123 / 2 / 1 / Solution

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2023/iii/paper-123/2/1/solution