Greatest common divisors of iterates of polynomials

Liang-Chung Hsia, Thomas J. Tucker

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

Following work of Bugeaud, Corvaja, and Zannier for integers, Ailon and Rudnick prove that for any multiplicatively independent polynomials, a,bεℂℂ[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,gεℂℂ[x] are compositionally independent polynomials and c(x)εℂℂ[x], then there are at most finitely many λ with the property that there is an n such that (x-λ) divides gcd(fon(x)-c(x),gon(x)-c(x)).

Original languageEnglish
Pages (from-to)1437-1459
Number of pages23
JournalAlgebra and Number Theory
Volume11
Issue number6
DOIs
Publication statusPublished - 2017 Jan 1

Fingerprint

Highest common factor
Iterate
Polynomial
Divides
Analogue
Integer
Theorem

Keywords

  • Composition
  • Equidstribution
  • Gcd
  • Heights

ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this

Greatest common divisors of iterates of polynomials. / Hsia, Liang-Chung; Tucker, Thomas J.

In: Algebra and Number Theory, Vol. 11, No. 6, 01.01.2017, p. 1437-1459.

Research output: Contribution to journalArticle

Hsia, Liang-Chung ; Tucker, Thomas J. / Greatest common divisors of iterates of polynomials. In: Algebra and Number Theory. 2017 ; Vol. 11, No. 6. pp. 1437-1459.
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