A random polynomial with multiplicative coefficients is almost surely irreducible

Abstract

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 $1-O(d^{-1/2+\epsilon })$.

19 pages, revision based on referee's report.Author Accepted Manuscript. To appear in IMRN