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Simplest quartic and simplest sextic Thue equations over imaginary quadratic fields

The families of simplest cubic, simplest quartic and simplest sextic fields and the related Thue equations are well known. The family of simplest cubic Thue equations has already been studied in the relative case, over imaginary quadratic fields. We observe a similar extension of simplest quartic and simplest sextic Thue equations over imaginary quadratic fields. We explicitly give the solutions of these infinite parametric families of Thue equations over arbitrary imaginary quadratic fields. Our result is obtained by an efficient method which allows us to reduce the resolution of relative Thue inequalities |F(x, y)|<K to the resolution of absolute Thue inequalities in the case when the corresponding polynomial f(x)=F(x, 1) has real roots. This is joint work with I. Gaal and L. Remete

relative Thue equations, Thue inequalities, simplest quartic fields, simplest sextic fields

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