A random polynomial with multiplicative coefficients is almost surely irreducible

Péter P. Varjú; Max Wenqiang Xu

doi:10.1093/imrn/rnag178

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arXiv · 2511.04240

A random polynomial with multiplicative coefficients is almost surely irreducible

Péter P. Varjú·Max Wenqiang Xu

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Abstract

Assume that the Riemann hypothesis holds for Dedekind zeta functions. Under this assumption, we prove that a degree $d$ polynomial with random multiplicative $\pm1$ coefficients is irreducible in $\mathbb{Z}[x]$ with probability $1-O(d^{-1/2+\varepsilon})$.

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Péter P. Varjú, Max Wenqiang Xu. 2025-11-06. A random polynomial with multiplicative coefficients is almost surely irreducible. https://doi.org/10.1093/imrn%2Frnag178

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