For a set $S$ of prime ideals, its <Dirichlet density> is
$$
\delta(S)=\lim_{s\to1^+}
\frac{\sum_{\mathfrak p\in S}N\mathfrak p^{-s}}
{\log(1/(s-1))}
$$
when this limit exists.

Solution

Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 123 / 5 / a / Solution

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A set $S$ of prime ideals has Dirichlet density
$$
\delta(S)=\lim_{s\to1^+}
\frac{\sum_{\mathfrak p\in S}N\mathfrak p^{-s}}
{\log(1/(s-1))},
$$
when the limit exists.


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