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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality 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 roots of unity in orbits of rational functions
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by Alina Ostafe PDF
Proc. Amer. Math. Soc. 145 (2017), 1927-1936 Request permission

Abstract:

We consider a large class of univariate rational functions over a number field $\mathbb {K}$, including all polynomials over $\mathbb {K}$, and give a precise description of the exceptional set of such functions $h$ for which there are infinitely many initial points in the cyclotomic closure $\mathbb {K}^c$ for which the orbit under iterations of $h$ contains a root of unity. Our results are similar to previous results of Dvornicich and Zannier describing all polynomials having infinitely many preperiodic points in $\mathbb {K}^c$. We also pose several open questions.
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Additional Information
  • Alina Ostafe
  • Affiliation: School of Mathematics and Statistics, University of New South Wales, Sydney NSW 2052, Australia
  • MR Author ID: 884181
  • Email: alina.ostafe@unsw.edu.au
  • Received by editor(s): May 17, 2016
  • Received by editor(s) in revised form: July 3, 2016
  • Published electronically: November 3, 2016
  • Communicated by: Matthew A. Papanikolas
  • © Copyright 2016 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 145 (2017), 1927-1936
  • MSC (2010): Primary 11R18, 37F10
  • DOI: https://doi.org/10.1090/proc/13433
  • MathSciNet review: 3611309