November 9, 2025Open Access

A random polynomial with multiplicative coefficients is almost surely irreducible

Key Points

Irreducibility in random degree d polynomials can be ensured with high probability under the Riemann hypothesis.
The analysis indicates probability of irreducibility approaches 1, minus an error term dependent on d.
Issues of polynomials and multiplicative coefficients are significant in understanding their irreducibility properties.
Conclusion emphasizes the relevance of the Riemann hypothesis and its implications in the field of number theory.

Abstract

Assume that the Riemann hypothesis holds for Dedekind zeta functions. Under this assumption, we prove that a degree d polynomial with random multiplicative 1 coefficients is irreducible in Zx with probability 1-O (d^-1/2+).

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Cite This Study

Varjú et al. (Thu,) studied this question.

synapsesocial.com/papers/690fdcdaf60c54d04ea37ebb https://doi.org/https://doi.org/10.48550/arxiv.2511.04240

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