On the Length of Critical Orbits of Stable Quadratic Polynomials
Alina Ostafe, Igor E. Shparlinski · arXiv (Cornell University) · 2009
We use the Weil bound of multiplicative character sums together with some recent results of N. Boston and R. Jones, to show that the critical orbit of quadratic polynomials over a finite field of $q$ elements is of length $O(q^{3/4})$, improving upon the trivial bound $q$.