Mixed degree number field computations

John W. Jones, David P. Roberts

Research output: Contribution to journalArticlepeer-review

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 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: GL 3(2 ) of smallest absolute discriminant.

Original languageEnglish (US)
Pages (from-to)47-66
Number of pages20
JournalRamanujan Journal
Volume47
Issue number1
DOIs
StatePublished - Oct 1 2018

Bibliographical note

Funding 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.

Publisher Copyright:
© 2018, Springer Science+Business Media, LLC, part of Springer Nature.

Keywords

  • Discriminant
  • Galois group
  • Number field
  • Ramification

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