Computing all elements of given index in sextic fields with a cubic subfield. (English) Zbl 1081.11022

The author develops a method for the computation of all elements of given index in sextic fields containing a cubic subfield. He follows well known ideas [see I. Gaál, Diophantine equations and power integral bases (Birkhäuser, Boston) (2002; Zbl 1016.11059) for a survey]. As usual, he transforms the index form equation into a unit equation. In the worst case, this requires to solve such an equation over a totally real field of Galois group \(S_4 \times C_2\) which contains 11 fundamental units. One example for an index 1 is included.


11D57 Multiplicative and norm form equations
11Y50 Computer solution of Diophantine equations
11Y40 Algebraic number theory computations
11R21 Other number fields


Zbl 1016.11059


Full Text: EuDML


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