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2019 Irreducibility of iterates of post-critically finite quadratic polynomials over $\mathbb {Q}$
Vefa Goksel
Rocky Mountain J. Math. 49(7): 2155-2174 (2019). DOI: 10.1216/RMJ-2019-49-7-2155

Abstract

In this paper, we classify, up to three possible exceptions, all monic, post-critically finite quadratic polynomials $f(x)\in \mathbb {Z}[x]$ with an iterate reducible module every prime, but all of whose iterates are irreducible over $\mathbb {Q}$. In particular, we obtain infinitely many new examples of the phenomenon studied by Jones. While doing this, we also find, up to three possible exceptions, all integers $a$ such that all iterates of the quadratic polynomial ${(x+a)^2-a-1}$ are irreducible over $\mathbb {Q}$, which answers a question posed in by Ayad and McQuillan, except for three values of $a$. Finally, we make a conjecture that suggests a necessary and sufficient condition for the stability of any monic, post-critically finite quadratic polynomial over any field of characteristic $\neq 2$.

Citation

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Vefa Goksel. "Irreducibility of iterates of post-critically finite quadratic polynomials over $\mathbb {Q}$." Rocky Mountain J. Math. 49 (7) 2155 - 2174, 2019. https://doi.org/10.1216/RMJ-2019-49-7-2155

Information

Published: 2019
First available in Project Euclid: 8 December 2019

zbMATH: 07152858
MathSciNet: MR4039963
Digital Object Identifier: 10.1216/RMJ-2019-49-7-2155

Subjects:
Primary: 11R09, 37P15

Rights: Copyright © 2019 Rocky Mountain Mathematics Consortium

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Vol.49 • No. 7 • 2019
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