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On the length of critical orbits of stable quadratic polynomials
Author(s):
Alina
Ostafe;
Igor
E.
Shparlinski
Journal:
Proc. Amer. Math. Soc.
138
(2010),
2653-2656.
MSC (2010):
Primary 11L40, 11T06, 37P25
Posted:
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  elements is of length  , improving upon the trivial bound  .
References:
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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:
10.1090/S0002-9939-10-10404-3
PII:
S 0002-9939(10)10404-3
Received by editor(s):
September 22, 2009
Posted:
March 30, 2010
Communicated by:
Ken Ono
Copyright of article:
Copyright
2010,
American Mathematical Society
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