I'm reading P.J. Weinberger's article "Finding the Number of Factors of a Polynomial" (Journal of Algorithms, 5, 1984) and I can't fully understand an assertion on primes of (inertial) degree one in the ring of algebraic integers of a number field. What is stated is that, given a number field $K$ and a prime $p$, the average number of primes of degree one of $\mathcal{O}_{K}$ which lie above $p$ is one, due to prime number theorem for number fields. Why is this true?
2026-04-12 00:22:13.1775953333
average number of primes of degree one which lie above p
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