Greatest Prime Divisors of Polynomial Values over Function Fields

TL;DR

This paper establishes a lower bound on the degree of the greatest prime divisor of polynomial values over function fields, extending classical number theory results to the function field setting.

Contribution

It provides a new lower bound for the greatest prime divisor of polynomial values over function fields, a significant extension of classical number theory results.

Findings

Lower bound for prime divisor degree in function fields

Extension of classical number theory to function fields

Results applicable under certain polynomial restrictions

Abstract

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.