On the frequency of integer polynomials with a given number of close roots

In the paper is considered the relation between number of integer polynomials of some degree having a given number of close real roots on the upper bound for diameter of this root cluster. There was established the asymptotics of that relation as the root cluster diameter tends to zero and maximal height of polynomials tends to infinity. The lower bound for the number of integer polynomial of given degree with bounded height and bounded discriminant is obtained.