Periods of Iterated Rational Functions over a Finite Field
Number Theory
2017-01-10 v3 Combinatorics
Abstract
Choose a random degree d poly f with coefficients in a finite field F. We estimate the ultimate period of f under compositional iteration. We also determine the joint distribution of the small cycle lengths in the graph with edges (x,f(x)), x in F. The proofs use Lagrange interpolation and the method of factorial moments.
Keywords
Cite
@article{arxiv.1508.04193,
title = {Periods of Iterated Rational Functions over a Finite Field},
author = {Charles Burnette and Eric Schmutz},
journal= {arXiv preprint arXiv:1508.04193},
year = {2017}
}
Comments
Improved results and exposition. To appearing IJNT