English

Dynamical Irreducibility of Certain Families of Polynomials over Finite Fields

Number Theory 2024-09-17 v1 Dynamical Systems

Abstract

We determine necessary and sufficient conditions for unicritical polynomials to be dynamically irreducible over finite fields. This result extends the results of Boston-Jones and Hamblen-Jones-Madhu regarding the dynamical irreducibility of particular families of unicritical polynomials. We also investigate dynamical irreducibility conditions for cubic and shifted linearized polynomials.

Keywords

Cite

@article{arxiv.2409.10467,
  title  = {Dynamical Irreducibility of Certain Families of Polynomials over Finite Fields},
  author = {Tori Day and Rebecca DeLand and Jamie Juul and Cigole Thomas and Bianca Thompson and Bella Tobin},
  journal= {arXiv preprint arXiv:2409.10467},
  year   = {2024}
}