On roots of unity in orbits of rational functions

Alina Ostafe

doi:10.1090/proc/13433

On roots of unity in orbits of rational functions

Alina Ostafe^*

^*Corresponding author for this work

Research output: Contribution to journal › Article

7 Citations (Scopus)

Abstract

We consider a large class of univariate rational functions over a number field K, including all polynomials over 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 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 K^c. We also pose several open questions.

Original language	English
Pages (from-to)	1927-1936
Number of pages	10
Journal	Proceedings of the American Mathematical Society
Volume	145
Issue number	5
DOIs	https://doi.org/10.1090/proc/13433
Publication status	Published - 2017
Externally published	Yes

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AB - We consider a large class of univariate rational functions over a number field K, including all polynomials over 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 Kc 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 Kc. We also pose several open questions.

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