Polynomials with a given discriminant over fields of algebraic functions of positive characteristic (Q1814773)

In a series of papers \textit{K. Györy} obtained effective results on polynomials with given discriminants. He showed that a polynomial with given discriminant is equivalent to a polynomial of bounded height [cf. e.g. Acta Arith. 23, 419-426 (1973; Zbl 0269.12001)]. \textit{I. Gaál} proved an analogous effective result over function fields of characteristic 0 [Acta Math. Hung. 52, 133-146 (1988; Zbl 0661.12005)]. In the present paper the author considers the same problem over function fields of positive characteristic. Using an extension of Mason's inequality on unit equations in two variables to the case of positive characteristic, the author gives effective results on polynomials with given discriminants over algebraic function fields of positive characteristic. Note that these theorems are not the direct analogues of the corresponding results in the number field case, since the same statements do not remain valid in the present situation. Corresponding questions, like elements with given discriminants, power integral bases are also considered in the paper.