## Septic fields with discriminant $\pm 2^a 3^b$

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- by John W. Jones and David P. Roberts;
- Math. Comp.
**72**(2003), 1975-1985 - DOI: https://doi.org/10.1090/S0025-5718-03-01510-2
- Published electronically: February 3, 2003
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## Abstract:

We classify septic number fields which are unramified outside of $\{\infty ,2, 3\}$ by a targeted Hunter search; there are exactly $10$ such fields, all with Galois group $S_7$. We also describe separate computations which strongly suggest that none of these fields come from specializing septic genus zero three-point covers.## References

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## Bibliographic Information

**John W. Jones**- Affiliation: Department of Mathematics and Statistics, Arizona State University, Box 871804, Tempe, Arizona 85287
- Email: jj@asu.edu
**David P. Roberts**- Affiliation: Division of Science and Mathematics, University of Minnesota-Morris, Morris, Minnesota 56267
- Email: roberts@mrs.umn.edu
- Received by editor(s): August 27, 2001
- Received by editor(s) in revised form: April 4, 2002
- Published electronically: February 3, 2003
- © Copyright 2003 American Mathematical Society
- Journal: Math. Comp.
**72**(2003), 1975-1985 - MSC (2000): Primary 11Y40
- DOI: https://doi.org/10.1090/S0025-5718-03-01510-2
- MathSciNet review: 1986816