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Dedekind zeta function

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For a number field of signature $(r_1,r_2)$, roots-of-unity count $w_K$, regulator $R_K$, class number $h_K$, and discriminant $d_K$,
$$
\operatorname*{Res}_{s=1}\zeta_K(s)
=\frac{2^{r_1}(2\pi)^{r_2}h_KR_K}{w_K\sqrt{|d_K|}}.
$$


Analytic class number formula

Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 123 / 3 / f / Solution

Analytic class number formula

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Analytic class number formula

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