This analysis shows that random degree d polynomials with multiplicative coefficients are irreducible with probability, suggesting implications for number theory.
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 Z[x] with probability 1-O(d-1/2+ε).
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Varjú et al. (2025) studied this question.