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The number of ramified primes in number fields of small degree


Authors: Robert J. Lemke Oliver and Frank Thorne
Journal: Proc. Amer. Math. Soc. 145 (2017), 3201-3210
MSC (2010): Primary 11K65, 11R16, 11R21
DOI: https://doi.org/10.1090/proc/13467
Published electronically: April 26, 2017
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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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Additional Information

Robert J. Lemke Oliver
Affiliation: Department of Mathematics, Tufts University, 503 Boston Avenue, Medford, Massachusetts 02155
Email: robert.lemke_oliver@tufts.edu

Frank Thorne
Affiliation: Department of Mathematics, University of South Carolina, 1523 Greene Street, Columbia, South Carolina 29201
Email: thorne@math.sc.edu

DOI: https://doi.org/10.1090/proc/13467
Received by editor(s): July 26, 2016
Published electronically: April 26, 2017
Additional Notes: The first author was supported by an NSF Mathematical Sciences Postdoctoral Research Fellowship at Stanford University
The second author was partially supported by the National Science Foundation under Grant No. DMS-1201330.
Communicated by: Ken Ono
Article copyright: © Copyright 2017 Robert Lemke Oliver and Frank Thorne