"Reducible polynomials of bounded height"

We obtain an asymptotic formula for the number of reducible integer polynomials of degree $d$ and of height at most $T$ as $T \to \infty$. For each $d \geq 3$ the main term turns out to be of the form $c_d T^d$, where the constant $c_d$ is given in terms of some infinite Dirichlet series involving volumes of symmetric convex bodies in $R^d$. Earlier results in this direction were given by van der Waerden (1934), Polya and Szego, Chela (1963), Dorge (1965) and Kuba (2009).