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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the length of critical orbits of stable quadratic polynomials


Authors: Alina Ostafe and Igor E. Shparlinski
Journal: Proc. Amer. Math. Soc. 138 (2010), 2653-2656
MSC (2010): Primary 11L40, 11T06, 37P25
Published electronically: March 30, 2010
MathSciNet review: 2644881
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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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Additional Information

Alina Ostafe
Affiliation: Institut für Mathematik, Universität Zürich, Winterthurerstrasse 190, CH-8057, Zürich, Switzerland
Email: alina.ostafe@math.uzh.ch

Igor E. Shparlinski
Affiliation: Department of Computing, Macquarie University, Sydney, NSW 2109, Australia
Email: igor@ics.mq.edu.au

DOI: http://dx.doi.org/10.1090/S0002-9939-10-10404-3
PII: S 0002-9939(10)10404-3
Received by editor(s): September 22, 2009
Published electronically: March 30, 2010
Communicated by: Ken Ono
Article copyright: © Copyright 2010 American Mathematical Society