A <Dirichlet character> modulo $m$ is a homomorphism
$$
\chi:(\mathbb Z/m\mathbb Z)^\times\to\mathbb C^\times.
$$
Extend it 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 / 2024 / iii / Paper 123 / 3 / a / Solution

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2024/iii/paper-123/3/a/solution