For a function field K and fixed polynomial F ∈ K[x] and varying f ∈ 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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-aa165-4-4,
author = {Alexei Entin},
title = {Greatest prime divisors of polynomial values over function fields},
journal = {Acta Arithmetica},
volume = {166},
year = {2014},
pages = {339-349},
zbl = {1322.11121},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa165-4-4}
}
Alexei Entin. Greatest prime divisors of polynomial values over function fields. Acta Arithmetica, Tome 166 (2014) pp. 339-349. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa165-4-4/