A quantitative version of Northcott's theorem on points of bounded height: The function field case

Abstract Let be a finite algebraic extension of the field of rational functions in one indeterminate over a finite field and let denote an algebraic closure of . For given integers and we count points in projective space with absolute logarithmic height and generating an extension of degree over . Specifically, we derive an asymptotic estimate for the number of such points as when and orders of growth for the number of such points when .