JP Journal of Algebra, Number Theory and Applications
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Abstract: Using standard techniques, we study the existence of
power integral bases and the behaviour of minimal indices of pure cubic fields
of type up to
discriminant and respectively.
Such calculations for these special fields are performed here for the first
time. This yields to solve cubic Thue equations, that may have extreme
coefficients in some examples. Based on our computational results on index form
equations in these fields, we consider the frequency of fields with power
integral bases and the average behaviour of minimal indices.
Keywords and phrases: pure cubic fields, power integral bases, minimal indices.
