Irreducibility of Littlewood polynomials of special degrees

2023/08/09 by Lior Bary‐Soroker, David Hokken, Bary-Soroker, Lior +4 · 1 citation
Mathematics · #11R09 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Mathematical Dynamics and Fractals #Number Theory (math.NT) #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.2308.04878

openalex publication_date 2023/08/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let f be sampled uniformly at random from the set of degree n polynomials whose coefficients lie in \ ± 1\. A folklore conjecture, known to hold under GRH, states that the probability that f is irreducible tends to 1 as n goes to infinity. We prove unconditionally that \limsup_{n → ∞} ℙ(f is irreducible) = 1.

Cited by

• Irreducibility and Galois groups of random reciprocal polynomials of large degree

Related

• Irreducibility of random polynomials of ℤ[X]
• Irreducibility of Polynomials with Square Coefficients over Finite Fields
• Irreducibility of polynomials with random multiplicative coefficients revisited
• On the probability of irreducibility of random polynomials with integer coefficients
• Irreducibility of Random Polynomials