Greatest Prime Divisors of Polynomial Values over Function Fields

Alexei Entin

Greatest Prime Divisors of Polynomial Values over Function Fields

Number Theory 2013-08-15 v3

Authors: Alexei Entin

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.

Keywords

polynomial theory polynomials over finite fields upper bounds

Cite

@article{arxiv.1307.0766,
  title  = {Greatest Prime Divisors of Polynomial Values over Function Fields},
  author = {Alexei Entin},
  journal= {arXiv preprint arXiv:1307.0766},
  year   = {2013}
}

Related papers

View all related →