Quartic Fields

István Gaál
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István Gaál: University of Debrecen, Institute of Mathematics and Informatics

Chapter 6 in Diophantine Equations and Power Integral Bases, 2002, pp 55-77 from Springer

Abstract: 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.

Date: 2002
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DOI: 10.1007/978-1-4612-0085-7_6

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