The density of discriminants of S3-sextic number fields

Manjul Bhargava; Melanie Matchett Wood

doi:10.1090/S0002-9939-07-09171-X

The density of discriminants of S₃-sextic number fields

Manjul Bhargava, Melanie Matchett Wood

Mathematics

Research output: Contribution to journal › Article › peer-review

19 Scopus citations

Abstract

We prove an asymptotic formula for the number of sextic number fields with Galois group S₃ 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 S₃-sextic extensions of any number field, and also when finitely many local completions have been specified for the sextic extensions.

Original language	English (US)
Pages (from-to)	1581-1587
Number of pages	7
Journal	Proceedings of the American Mathematical Society
Volume	136
Issue number	5
DOIs	https://doi.org/10.1090/S0002-9939-07-09171-X
State	Published - May 2008

All Science Journal Classification (ASJC) codes

Mathematics(all)
Applied Mathematics

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abstract = "We prove an asymptotic formula for the number of sextic number fields with Galois group S3 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 S3-sextic extensions of any number field, and also when finitely many local completions have been specified for the sextic extensions.",

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AB - We prove an asymptotic formula for the number of sextic number fields with Galois group S3 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 S3-sextic extensions of any number field, and also when finitely many local completions have been specified for the sextic extensions.

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The density of discriminants of S₃-sextic number fields

Abstract

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