Vol. 11, No. 6, 2017

Download this article
Download this article For screen
For printing
Recent Issues

Volume 16
Issue 2, 231–519
Issue 1, 1–230

Volume 15, 10 issues

Volume 14, 10 issues

Volume 13, 10 issues

Volume 12, 10 issues

Volume 11, 10 issues

Volume 10, 10 issues

Volume 9, 10 issues

Volume 8, 10 issues

Volume 7, 10 issues

Volume 6, 8 issues

Volume 5, 8 issues

Volume 4, 8 issues

Volume 3, 8 issues

Volume 2, 8 issues

Volume 1, 4 issues

The Journal
About the Journal
Editorial Board
Editors’ Interests
Submission Guidelines
Submission Form
Policies for Authors
Ethics Statement
ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
Author Index
To Appear
Other MSP Journals
This article is available for purchase or by subscription. See below.
Greatest common divisors of iterates of polynomials

Liang-Chung Hsia and Thomas J. Tucker

Vol. 11 (2017), No. 6, 1437–1459

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)).

PDF Access Denied

However, your active subscription may be available on Project Euclid at

We have not been able to recognize your IP address as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.

Please contact your institution's librarian suggesting a subscription, for example by using our journal-recom­mendation form. Or, visit our subscription page for instructions on purchasing a subscription.

You may also contact us at contact@msp.org
or by using our contact form.

Or, you may purchase this single article for USD 40.00:

gcd, composition, heights, equidstribution
Mathematical Subject Classification 2010
Primary: 37P05
Secondary: 14G25
Received: 7 December 2016
Revised: 11 April 2017
Accepted: 13 May 2017
Published: 16 August 2017
Liang-Chung Hsia
Department of Mathematics
National Taiwan Normal University
Thomas J. Tucker
Department of Mathematics
University of Rochester
Rochester, NY 14627
United States