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On the length of critical orbits of stable quadratic polynomials. (English) Zbl 1268.11155
Summary: 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 \(q\).

MSC:
11T06 Polynomials over finite fields
37P25 Dynamical systems over finite ground fields
11L40 Estimates on character sums
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