Abstract
Following work of Bugeaud, Corvaja, and Zannier for integers, Ailon and Rudnick prove that for any multiplicatively independent polynomials, , there is a polynomial such that for all , we have
We prove a compositional analog of this theorem, namely that if are compositionally independent polynomials and , then there are at most finitely many with the property that there is an such that divides .
Citation
Liang-Chung Hsia. Thomas Tucker. "Greatest common divisors of iterates of polynomials." Algebra Number Theory 11 (6) 1437 - 1459, 2017. https://doi.org/10.2140/ant.2017.11.1437
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