Irreducibility of polynomials with random multiplicative coefficients revisited

Oleksiy Klurman; Vlad Matei

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arXiv · 2511.10359

Irreducibility of polynomials with random multiplicative coefficients revisited

Oleksiy Klurman·Vlad Matei

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Abstract

We show that for a random polynomial \[ F(X) = \sum_{n=1}^{N} f(n) X^{n-1}, \] where $f(n)$ is a random completely multiplicative function taking values in $\{\pm 1\}$, one has \[ \limsup_{N \to \infty} \mathbb{P}\big[F(X) \text{ is irreducible}\big] = 1. \]

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Oleksiy Klurman, Vlad Matei. 2025-11-13. Irreducibility of polynomials with random multiplicative coefficients revisited. https://arxiv.org/abs/2511.10359

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