Unlikely intersections over finite fields: polynomial orbits in small subgroups
Number Theory
2019-09-12 v2 Dynamical Systems
Abstract
We estimate the frequency of polynomial iterations which falls in a given multiplicative subgroup of a finite field of elements. We also give a lower bound on the size of the subgroup which is multiplicatively generated by the first elements in an orbit. We derive these from more general results about sequences of compositions or a fixed set of polynomials.
Cite
@article{arxiv.1904.12621,
title = {Unlikely intersections over finite fields: polynomial orbits in small subgroups},
author = {László Mérai and Igor E. Shparlinski},
journal= {arXiv preprint arXiv:1904.12621},
year = {2019}
}