## On the Length of Critical Orbits of Stable Quadratic Polynomials

##### Authors
Ostafe, Alina
Shparlinski, Igor E.
##### Description
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 $q$.
##### Keywords
Mathematics - Number Theory, 11L40, 11T06, 37F10