Eisenstein series on weakly spherical homogeneous spaces of GL(n)

A homogeneous space of a reductive group is called weakly spherical if the action of some proper parabolic subgroup is prehomogeneous. We associate Dirichlet series with weakly spherical homogeneous spaces defined over the rational number field and prove their functional equations in the case where the space under consideration is a homogeneous space of the general linear group.