The number of ramified primes in number fields of small degree

The number of ramified primes in number fields of small degree

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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Veröffentlicht in:Proceedings of the American Mathematical Society 2017-08, Vol.145 (8), p.3201-3210
Hauptverfasser: OLIVER, ROBERT J. LEMKE, THORNE, FRANK
Format: Artikel
Sprache:eng
Schlagworte:
A. ALGEBRA, NUMBER THEORY, AND COMBINATORICS
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Zusammenfassung: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.
ISSN:0002-9939
1088-6826
DOI:10.1090/proc/13467