Let
$$
U_{\mathfrak m,1}
=\{u\in\mathcal O_K^\times:
u\equiv1\pmod{\mathfrak m_0},\
\sigma(u)>0\text{ for }\sigma\mid\mathfrak m_\infty\}.
$$
The <ray class number formula> is
$$
\boxed{|\operatorname{Cl}_{\mathfrak m}(K)|
=h_K\frac{2^{|\mathfrak m_\infty|}
N\mathfrak m_0
\prod_{\mathfrak p\mid\mathfrak m_0}(1-N\mathfrak p^{-1})}
{[\mathcal O_K^\times:U_{\mathfrak m,1}]}.}
$$

Solution

Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 123 / 1 / c / Solution

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2024/iii/paper-123/1/c/solution