A random polynomial with multiplicative coefficients is almost surely irreducible
Abstract
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 $1-O(d^{-1/2+\varepsilon })$.
Fields of Study & Subjects
Analytic Number Theory Research
Geometry and complex manifolds
Meromorphic and Entire Functions
Publication details
- Journal / source
- International Mathematics Research Notices
- Volume
- 2026
- Issue
- 16
- Publication date
- 1 August 2026
- Language
- EN