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2017 Greatest common divisors of iterates of polynomials
Liang-Chung Hsia, Thomas Tucker
Algebra Number Theory 11(6): 1437-1459 (2017). DOI: 10.2140/ant.2017.11.1437

Abstract

Following work of Bugeaud, Corvaja, and Zannier for integers, Ailon and Rudnick prove that for any multiplicatively independent polynomials, a,b [x], there is a polynomial h such that for all n, we have

gcd(an 1,bn 1)|h

We prove a compositional analog of this theorem, namely that if f,g [x] are compositionally independent polynomials and c(x) [x], then there are at most finitely many λ with the property that there is an n such that (x λ) divides gcd(fn(x) c(x),gn(x) c(x)).

Citation

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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

Information

Received: 7 December 2016; Revised: 11 April 2017; Accepted: 13 May 2017; Published: 2017
First available in Project Euclid: 16 November 2017

zbMATH: 06763331
MathSciNet: MR3687102
Digital Object Identifier: 10.2140/ant.2017.11.1437

Subjects:
Primary: 37P05
Secondary: 14G25

Rights: Copyright © 2017 Mathematical Sciences Publishers

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Vol.11 • No. 6 • 2017
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