English

On the Length of Critical Orbits of Stable Quadratic Polynomials

Number Theory 2009-09-28 v3

Abstract

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 qq elements is of length O(q3/4)O(q^{3/4}), improving upon the trivial bound qq.

Keywords

Cite

@article{arxiv.0909.3972,
  title  = {On the Length of Critical Orbits of Stable Quadratic Polynomials},
  author = {Alina Ostafe and Igor E. Shparlinski},
  journal= {arXiv preprint arXiv:0909.3972},
  year   = {2009}
}