Radical Dynamical Monogenicity

2023/06/20 by Hanson Smith, Smith, Hanson
Mathematics · #11R04 #11R21 #37P05 #Advanced Differential Equations and Dynamical Systems #Advanced Topics in Algebra #FOS: Mathematics #Number Theory (math.NT) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2306.11815

openalex publication_date 2023/06/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let a be an integer and p a prime so that f(x)=x^p-a is irreducible. Write fⁿ(x) to indicate the n-fold composition of f(x) with itself. We study the monogenicity of number fields defined by roots of fⁿ(x) and give necessary and sufficient conditions for a root of fⁿ(x) to yield a power integral basis for each n≥ 1.

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