On a 3-variable Catalan equation over function fields

Let [Formula: see text] be a smooth projective curve of genus [Formula: see text] over an algebraically closed field [Formula: see text] of characteristic zero. For integers [Formula: see text] sufficiently large and [Formula: see text], we provide a bound for the heights of solutions in the function field [Formula: see text] to the equation [Formula: see text], where [Formula: see text] are nonzero elements of [Formula: see text]. Our strategy centers around a greatest common divisor method by