May 7, 2024Open Access

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

Key Points

Key points are not available for this paper at this time.

Abstract

Let f (t₁, , tᵣ, X) Zt₁, , tᵣ, X be irreducible and let a₁, , aᵣ Z \0, 1\. Under a necessary ramification assumption on f, and conditionally on the Generalized Riemann Hypothesis, we show that for almost all integers n₁, , nᵣ, the polynomial f (a₁^n₁, , aᵣ^nᵣ, X) is irreducible in QX.

Read Full Paperexternally

KI fragen

Bookmark

View Full Paper

Cite This Study

Bary‐Soroker et al. (Tue,) studied this question.

synapsesocial.com/papers/68e6b4c2b6db6435876358f8 https://doi.org/https://doi.org/10.48550/arxiv.2405.04058

Also Consider

Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context:

1Variations on a theorem of Capelli2024
2Irreducible integer-valued polynomials with prescribed minimal power that factors non-uniquely2024
3Irreducibility properties of Carlitz' binomial coefficients for algebraic function fields2024 · 2 citations
4The irreducibility and monodromy of some families of linear series with imposed ramifications2024
5A random polynomial with multiplicative coefficients is almost surely irreducible2025

KI fragen

Bookmark

View Full Paper