Functional graphs of families of quadratic polynomials
Number Theory
2023-02-03 v2 Combinatorics
Abstract
We study functional graphs generated by several quadratic polynomials, acting simultaneously on a finite field of odd characteristic. We obtain several results about the number of leaves in such graphs. In particular, in the case of graphs generated by three polynomials, we relate the distribution of leaves to the Sato-Tate distribution of Frobenius traces of elliptic curves. We also present extensive numerical results which we hope may shed some light on the distribution of leaves for larger families of polynomials.
Keywords
Cite
@article{arxiv.2208.01885,
title = {Functional graphs of families of quadratic polynomials},
author = {Bernard Mans and Min Sha and Igor E. Shparlinski and Daniel Sutantyo},
journal= {arXiv preprint arXiv:2208.01885},
year = {2023}
}
Comments
30 pages