Poles of certain residual Eisenstein series of classical groups

Dihua Jiang, Baiying Liu and Lei Zhang

Vol. 264 (2013), No. 1, 83–123

DOI: 10.2140/pjm.2013.264.83

Abstract

We study the location of possible poles of a family of residual Eisenstein series on classical groups. Special types of residues of those Eisenstein series were used as key ingredients in the automorphic descent constructions of Ginzburg, Rallis and Soudry and in the refined constructions of Ginzburg, Jiang and Soudry. We study the conditions for the existence of other possible poles of those Eisenstein series and determine the possible Arthur parameters for the residual representations if they exist. Further properties of those residual representations and their applications to automorphic constructions will be considered in our future work.

Keywords

residual representations, Arthur parameters, Eisenstein series

Mathematical Subject Classification 2010

Primary: 11F70, 22E50

Secondary: 22E55, 11F72

Milestones

Received: 27 January 2012

Revised: 20 July 2012

Accepted: 26 July 2012

Published: 5 July 2013