engleski

Complete solutions to a family of quartic Thue inequalities over function fields

We consider a family of Thue inequalities defined over the field of functions C(T). In particular, we find all solutions of deg( X^{; ; 4}; ; -4cX^{; ; 3}; ; Y+(6c+2)X^{; ; 2}; ; Y^{; ; 2}; ; +4cXY^{; ; 3}; ; +Y^{; ; 4}; ; ) <= deg c, where the solutions X, Y come from the ring C[T] and the parameter c in C[T] is some non-constant polynomial.

Thue equations; function fields; continued fraction

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