Greatest prime divisors of polynomial values over function fields
Volume 165 / 2014
Acta Arithmetica 165 (2014), 339-349 MSC: Primary 11R58. DOI: 10.4064/aa165-4-4
For a function field $K$ and fixed polynomial $F\in K[x]$ and varying $f\in F$ (under certain restrictions) we give a lower bound for the degree of the greatest prime divisor of $F(f)$ in terms of the height of $f$, establishing a strong result for the function field analogue of a classical problem in number theory.