The number of ramified primes in number fields of small degree

Lemke Oliver, Robert; Thorne, Frank

doi:10.1090/proc/13467

The number of ramified primes in number fields of small degree
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by Robert J. Lemke Oliver and Frank Thorne PDF

Proc. Amer. Math. Soc. 145 (2017), 3201-3210

Abstract:

In this paper we investigate the distribution of the number of primes which ramify in number fields of degree $d \leq 5$. In analogy with the classical Erdős-Kac theorem, we prove for $S_d$-extensions that the number of such primes is normally distributed with mean and variance $\log \log X$.

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