On the images and poles of degenerate Eisenstein series for $GL_n(\mathbb A_{\mathbb Q})$ and $GL_n(\mathbb R)$

TL;DR

This paper analyzes the poles and images of degenerate Eisenstein series for general linear groups over the adeles and real numbers, providing a detailed understanding of their analytic properties and singularities.

Contribution

It determines the poles and images of degenerate Eisenstein series for $GL_n$ over adeles and real numbers, extending previous knowledge on their analytic structure.

Findings

Identified poles in the right-half plane for Eisenstein series over adeles.

Determined the images of these Eisenstein series.

Extended results to Eisenstein series over real numbers.

Abstract

I this paper we determine poles in the right--half plane and images of degenerate Eisenstein series for $GL_n(\Bbb A_\mathbb Q)$ induced from a character on a maximal parabolic subgroup. We apply those results to determine poles of degenerate Eisenstein series for $GL_n(\Bbb R)$.