On the length of critical orbits of stable quadratic polynomials

Alina Ostafe; Igor E. Shparlinski

doi:10.1090/S0002-9939-10-10404-3

On the length of critical orbits of stable quadratic polynomials

Alina Ostafe^*, Igor E. Shparlinski

^*Corresponding author for this work

School of Computing

Research output: Contribution to journal › Article › peer-review

21 Citations (Scopus)

24 Downloads (Pure)

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

Original language	English
Pages (from-to)	2653-2656
Number of pages	4
Journal	Proceedings of the American Mathematical Society
Volume	138
Issue number	8
DOIs	https://doi.org/10.1090/S0002-9939-10-10404-3
Publication status	Published - Aug 2010

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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 q elements is of length O(q 3/4), improving upon the trivial bound q.",

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On the length of critical orbits of stable quadratic polynomials

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