The Odlyzko-Poonen Conjecture on Irreducibility of Random Polynomials

Source abstract

The Odlyzko-Poonen conjecture states that a monic polynomial of constant coefficient $1$ and with remaining coefficients chosen independently and uniformly from $\{0,1 \}$ is irreducible over the rational numbers with probability tending to one as the degree tends to infinity. We prove the Odlyzko-Poonen conjecture unconditionally.