A random polynomial with multiplicative coefficients is almost surely irreducible

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