On a Family of Thue Equations Over Function Fields

Many families of parametrized Thue equations over number fields have been solved recently. In this paper we consider for the first time a family of Thue equations over a polynomial ring. In particular, we calculate all solutions of X(X-Y)(X-(T+x)Y)+Y³=1+xT(1-T)X(X-Y)(X-(T+\xi)Y)+Y^3=1+\xi T(1-T) over \Bbb CT]{\Bbb C}T] for all x ? \Bbb C\xi\in{\Bbb C} .