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Monatshefte für Mathematik

, Volume 134, Issue 4, pp 331–336 | Cite as

Cubic Fields with Index 2

  • Blair K. Spearman
  • Kenneth S. Williams

Abstract.

 Let d be a squarefree integer with \(\) allowed. If \(\) (mod 8) it is shown that there do not exist any cubic fields with index 2 whose splitting field contains \(\). If \(\) (mod 8) it is shown that there exist infinitely many cubic fields with index 2 and minimal index 2 whose splitting field contains \(\).

2000 Mathematics Subject Classification: 11R16 
Key words: Cubic fields power basis index minimal index common index divisor discriminant 

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Copyright information

© Springer-Verlag Wien 2002

Authors and Affiliations

  • Blair K. Spearman
    • 1
  • Kenneth S. Williams
    • 2
  1. 1. Okanagan University College, Kelowna, B.C., CanadaCA
  2. 2. Carleton University, Ottawa, Ontario, CanadaCA

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