### 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.

Original language | English (US) |
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Pages (from-to) | 1581-1587 |

Number of pages | 7 |

Journal | Proceedings of the American Mathematical Society |

Volume | 136 |

Issue number | 5 |

DOIs | |

State | Published - May 1 2008 |

### All Science Journal Classification (ASJC) codes

- Mathematics(all)
- Applied Mathematics

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## Cite this

Bhargava, M., & Wood, M. M. (2008). The density of discriminants of S

_{3}-sextic number fields.*Proceedings of the American Mathematical Society*,*136*(5), 1581-1587. https://doi.org/10.1090/S0002-9939-07-09171-X