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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The density of discriminants of $ S_3$-sextic number fields


Authors: Manjul Bhargava and Melanie Matchett Wood
Journal: Proc. Amer. Math. Soc. 136 (2008), 1581-1587
MSC (2000): Primary 11R21, 11R45
Published electronically: October 12, 2007
MathSciNet review: 2373587
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Abstract: We prove an asymptotic formula for the number of sextic number fields with Galois group $ S_3$ and absolute discriminant $ <X$. In addition, we give an interpretation of the constant in the formula in terms of the asymptotic densities of given local completions among these sextic fields. Our proof gives analogous results when we count $ S_3$-sextic extensions of any number field, and also when finitely many local completions have been specified for the sextic extensions.


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Additional Information

Manjul Bhargava
Affiliation: Department of Mathematics, Princeton University, Princeton, New Jersey 08544

Melanie Matchett Wood
Affiliation: Department of Mathematics, Princeton University, Princeton, New Jersey 08544

DOI: http://dx.doi.org/10.1090/S0002-9939-07-09171-X
PII: S 0002-9939(07)09171-X
Received by editor(s): December 19, 2006
Received by editor(s) in revised form: March 24, 2007
Published electronically: October 12, 2007
Communicated by: Wen-Ching Winnie Li
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.