The number of ramified primes in number fields of small degree

Abstract

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

arXiv comment9 pages, to appear in Proceedings of the AMS