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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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
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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