Vol. 264, No. 1, 2013

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Poles of certain residual Eisenstein series of classical groups

Dihua Jiang, Baiying Liu and Lei Zhang

Vol. 264 (2013), No. 1, 83–123

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.

residual representations, Arthur parameters, Eisenstein series
Mathematical Subject Classification 2010
Primary: 11F70, 22E50
Secondary: 22E55, 11F72
Received: 27 January 2012
Revised: 20 July 2012
Accepted: 26 July 2012
Published: 5 July 2013
Dihua Jiang
School of Mathematics
University of Minnesota
Minneapolis, MN 55455
United States
Baiying Liu
School of Mathematics
University of Minnesota
Minneapolis, MN 55455
United States
Lei Zhang
Department of Mathematics
Boston College
Carney Hall, 140 Commonwealth Ave
Chestnut Hill, MA 02467
United States