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Quartic Fields

In: Diophantine Equations and Power Integral Bases

Author

Listed:
  • István Gaál

    (University of Debrecen, Institute of Mathematics and Informatics)

Abstract

In the cubic case the index form equation was a cubic Thue equation. In quartic fields, the index form equation has already degree six and three variables. The resolution of such an equation can yield a difficult problem. The main goal of this Chapter is to point out that in the quartic case the index form equation can be reduced to a cubic and some corresponding quartic Thue equations (see Section 6.1). This means that in fact the index form equations in quartic fields are not much harder to solve than in the cubic case.

Suggested Citation

  • István Gaál, 2002. "Quartic Fields," Springer Books, in: Diophantine Equations and Power Integral Bases, chapter 6, pages 55-77, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4612-0085-7_6
    DOI: 10.1007/978-1-4612-0085-7_6
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