On the irreducibility of f(2ⁿ,3^m,X) and other such polynomials

2024/05/07 by Lior Bary‐Soroker, Bary-Soroker, Lior, Daniele Garzoni +3
Mathematics · #11A07 #11R09 #12E25 #14G05 #Advanced Differential Equations and Dynamical Systems #Advanced Mathematical Theories #FOS: Mathematics #Meromorphic and Entire Functions #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2405.04058

openalex publication_date 2024/05/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let f(t₁, …, t_r, X)∈ ℤ[t₁, …, t_r,X] be irreducible and let a₁, …, a_r∈ ℤ \smallsetminus \0,± 1\. Under a necessary ramification assumption on f, and conditionally on the Generalized Riemann Hypothesis, we show that for almost all integers n₁, …, n_r, the polynomial f(a₁^n₁, …, a_r^n_r, X) is irreducible in ℚ[X].

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