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Mixed degree number field computations

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Abstract

We present a method for computing complete lists of number fields in cases where the Galois group, as an abstract group, appears as a Galois group in smaller degree. We apply this method to find the 25 octic fields with Galois group \({{\mathrm{PSL}}}_2(7)\) and smallest absolute discriminant. We carry out a number of related computations, including determining the octic field with Galois group \(2^3{:}{{\mathrm{GL}}}_3(2)\) of smallest absolute discriminant.

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Authors and Affiliations

  1. School of Mathematical and Statistical Sciences, Arizona State University, PO Box 871804, Tempe, AZ, 85287, USA

    John W. Jones

  2. Division of Science and Mathematics, University of Minnesota-Morris, Morris, MN, 56267, USA

    David P. Roberts

Authors
  1. John W. Jones
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  2. David P. Roberts
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Correspondence to John W. Jones.

Additional information

Roberts’ contribution was partially supported by the Simons Foundation through grant #209472 and, in its final stages, by the National Science Foundation, through grant DMS-1601350.

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Jones, J.W., Roberts, D.P. Mixed degree number field computations. Ramanujan J 47, 47–66 (2018). https://doi.org/10.1007/s11139-018-0024-9

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  • DOI: https://doi.org/10.1007/s11139-018-0024-9

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