The density of discriminants of S3-sextic number fields

Manjul Bhargava, Melanie Matchett Wood

Research output: Contribution to journalArticlepeer-review

19 Scopus citations


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 languageEnglish (US)
Pages (from-to)1581-1587
Number of pages7
JournalProceedings of the American Mathematical Society
Issue number5
StatePublished - May 2008

All Science Journal Classification (ASJC) codes

  • General Mathematics
  • Applied Mathematics


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