On the Length of Critical Orbits of Stable Quadratic Polynomials

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Ostafe, Alina
Shparlinski, Igor E.
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Abstract
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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
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