On the length of critical orbits of stable quadratic polynomials
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- by Alina Ostafe and Igor E. Shparlinski PDF
- Proc. Amer. Math. Soc. 138 (2010), 2653-2656 Request permission
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 $q$.References
Additional Information
- Alina Ostafe
- Affiliation: Institut für Mathematik, Universität Zürich, Winterthurerstrasse 190, CH-8057, Zürich, Switzerland
- MR Author ID: 884181
- Email: alina.ostafe@math.uzh.ch
- Igor E. Shparlinski
- Affiliation: Department of Computing, Macquarie University, Sydney, NSW 2109, Australia
- MR Author ID: 192194
- Email: igor@ics.mq.edu.au
- Received by editor(s): September 22, 2009
- Published electronically: March 30, 2010
- Communicated by: Ken Ono
- © Copyright 2010 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 138 (2010), 2653-2656
- MSC (2010): Primary 11L40, 11T06, 37P25
- DOI: https://doi.org/10.1090/S0002-9939-10-10404-3
- MathSciNet review: 2644881