TY - JOUR

T1 - Greatest common divisors of iterates of polynomials

AU - Hsia, Liang Chung

AU - Tucker, Thomas J.

N1 - Publisher Copyright:
© 2017 Mathematical Sciences Publishers.

PY - 2017

Y1 - 2017

N2 - 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)).

AB - 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)).

KW - Composition

KW - Equidstribution

KW - Gcd

KW - Heights

UR - http://www.scopus.com/inward/record.url?scp=85028043813&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85028043813&partnerID=8YFLogxK

U2 - 10.2140/ant.2017.11.1437

DO - 10.2140/ant.2017.11.1437

M3 - Article

AN - SCOPUS:85028043813

VL - 11

SP - 1437

EP - 1459

JO - Algebra and Number Theory

JF - Algebra and Number Theory

SN - 1937-0652

IS - 6

ER -