A <Dirichlet character> modulo $m$ is a group homomorphism
$$
\chi:(\mathbb Z/m\mathbb Z)^\times\longrightarrow\mathbb C^\times,
$$
extended periodically to $\mathbb Z$ by setting $\chi(n)=0$ when $(n,m)>1$. Its <Dirichlet L-function> is
$$
L(s,\chi)=\sum_{n\geq1}\frac{\chi(n)}{n^s}
=\prod_p(1-\chi(p)p^{-s})^{-1}
\qquad(\operatorname{Re}s>1).
$$

Solution

Past exam of the mathematics course of the University of Cambridge / 2023 / iii / Paper 123 / 2 / 2 / 3 / Solution

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2023/iii/paper-123/2/2/3/solution