Published In
International Journal of Number Theory
Document Type
Pre-Print
Publication Date
6-25-2024
Subjects
Galois Theory -- Arithmatic dynamics
Abstract
For a prime p, positive integers r,n, and a polynomial f with coefficients in Fpr, let Wp,r,n(f) = fn(Fpr) ∖ fn+1(Fpr). As n varies, the Wp,r,n(f) partition the set of strictly preperiodic points of the dynamical system induced by the action of f on Fpr. In this paper we compute statistics of strictly preperiodic points of dynamical systems induced by unicritical polynomials over finite fields by obtaining effective upper bounds for the proportion of Fpr lying in a given Wp,r,n(f). Moreover, when we generalize our definition of Wp,r,n(f), we obtain both upper and lower bounds for the resulting averages.
Rights
© Copyright the author(s) 2024
Locate the Document
DOI
10.1142/S1793042124501124
Persistent Identifier
https://archives.pdx.edu/ds/psu/42271
Citation Details
Published as: Andersen, A., & Garton, D. (2024). Preperiodic points of polynomial dynamical systems over finite fields. International Journal of Number Theory, 1–10. https://doi.org/10.1142/s1793042124501124
Description
This is the author’s version of a work that was accepted for publication. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published as: Preperiodic points of polynomial dynamical systems over finite fields. International Journal of Number Theory, 1–10.