On the images and poles of degenerate Eisenstein series for ${\rm GL}(n,\Bbb{A}_{\Bbb{Q}})$ and ${\rm GL}(n,\Bbb{R})$

Abstract

In this paper we determine poles in the right-half plane and images of degenerate Eisenstein series for ${\rm GL}_n(\Bbb{A}_{\Bbb{Q}})$ induced from a character on a maximal parabolic subgroup. We apply those results to determine poles of degenerate Eisenstein series for ${\rm GL}_n(\Bbb{R})$.