The density of discriminants of -sextic number fields

Authors:
Manjul Bhargava and Melanie Matchett Wood

Journal:
Proc. Amer. Math. Soc. **136** (2008), 1581-1587

MSC (2000):
Primary 11R21, 11R45

DOI:
https://doi.org/10.1090/S0002-9939-07-09171-X

Published electronically:
October 12, 2007

MathSciNet review:
2373587

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Abstract | References | Similar Articles | Additional Information

Abstract: We prove an asymptotic formula for the number of sextic number fields with Galois group and absolute discriminant . 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 -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:
https://doi.org/10.1090/S0002-9939-07-09171-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.