Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
131 tokens/sec
GPT-4o
10 tokens/sec
Gemini 2.5 Pro Pro
47 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Irreducibility of iterates of post-critically finite quadratic polynomials over $\mathbb{Q}$ (1710.06821v6)

Published 18 Oct 2017 in math.NT

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 in \cite{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 \cite{AyadMcdonald}, 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 $\neq 2$.

Summary

We haven't generated a summary for this paper yet.