DOI: 10.1093/imrn/rnag178 ISSN: 1073-7928

A random polynomial with multiplicative coefficients is almost surely irreducible

Péter P Varjú, Max Wenqiang Xu

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

More from our Archive