Past exam of the mathematics course of the University of Cambridge / 2023 / iii / Paper 123 / 3 / 3 / 5

Table of contents
- Solution 5

Solution

By Question 1, a prime ideal of

K

is principal exactly when it splits completely in the Hilbert class field

H_{K}

. Question 3(4) therefore gives

δ {p : p is principal} = \frac{1}{[ H _{K} : K ]} = \frac{1}{h _{K}} .

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