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


Authors: John W. Jones and David P. Roberts
Journal: Math. Comp. 72 (2003), 1975-1985
MSC (2000): Primary 11Y40
DOI: https://doi.org/10.1090/S0025-5718-03-01510-2
Published electronically: February 3, 2003
MathSciNet review: 1986816
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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.


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Additional 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

DOI: https://doi.org/10.1090/S0025-5718-03-01510-2
Received by editor(s): August 27, 2001
Received by editor(s) in revised form: April 4, 2002
Published electronically: February 3, 2003
Article copyright: © Copyright 2003 American Mathematical Society

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