Lower bounds for discriminants of polynomials

Let [Formula: see text] be a monic irreducible polynomial of degree [Formula: see text] having exactly [Formula: see text] real roots and [Formula: see text] complex roots with integer coefficients and [Formula: see text] be its polynomial discriminant. Suppose that [Formula: see text] is square-free. In this paper, we will give a lower bound for polynomial discriminants [Formula: see text] for given [Formula: see text].