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arXiv · 2308.04878

Irreducibility of Littlewood polynomials of special degrees

Lior Bary-Soroker·David Hokken·Gady Kozma·Bjorn Poonen
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Abstract

Let $f$ be sampled uniformly at random from the set of degree $n$ polynomials whose coefficients lie in $\{ \pm 1\}$. 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 $$\limsup_{n \to \infty} \mathbb{P}(f \text{ is irreducible}) = 1.$$

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Lior Bary-Soroker, David Hokken, Gady Kozma, Bjorn Poonen. 2023-08-09. Irreducibility of Littlewood polynomials of special degrees. https://arxiv.org/abs/2308.04878

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