Stable Polynomials over Finite Fields
Number Theory
2012-06-22 v1
Abstract
We use the theory of resultants of polynomials to study the stability of an arbitrary polynomial over a finite field, that is, the property of having all its iterates irreducible. This result partially generalises the quadratic polynomial case described by R. Jones and N. Boston. Moreover, for characteristic three, we show that certain polynomials of degree three are not stable. We also use the Weil bound for multiplicative character sums to estimate the number of stable arbitrary polynomials over finite fields of odd characteristic.
Cite
@article{arxiv.1206.4979,
title = {Stable Polynomials over Finite Fields},
author = {Domingo Gomez-Perez and Alejandro P. Nicolas and Alina Ostafe and Daniel Sadornil},
journal= {arXiv preprint arXiv:1206.4979},
year = {2012}
}