Journal of the Ramanujan Mathematical Society

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Residues of Eisenstein Series and Generalized Shalika Models for SO4n


Affiliations
1 School of Mathematics, University of Minnesota, Minneapolis, MN55455, United States
2 Department of Mathematics, East China Normal University, Shanghai 200062, China
     

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We introduce the generalized Shalika model for SO(4n), the split even orthogonal group of rank 2n, and develop the local and global compatibilities with the Shalika model for GL(2n), the general linear group of rank 2n. As result, we determine the existence of poles of certain Eisenstein series on SO(4n) in terms of the Shalika model on the cuspidal datum (GL(2n), π), and give a different proof for the determination of the pole at s = 1 of the exterior square L-function L(s, π,Λ2) in terms of the Shalika model on π.
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  • Residues of Eisenstein Series and Generalized Shalika Models for SO4n

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Authors

Dihua Jiang
School of Mathematics, University of Minnesota, Minneapolis, MN55455, United States
Yujun Qin
Department of Mathematics, East China Normal University, Shanghai 200062, China

Abstract


We introduce the generalized Shalika model for SO(4n), the split even orthogonal group of rank 2n, and develop the local and global compatibilities with the Shalika model for GL(2n), the general linear group of rank 2n. As result, we determine the existence of poles of certain Eisenstein series on SO(4n) in terms of the Shalika model on the cuspidal datum (GL(2n), π), and give a different proof for the determination of the pole at s = 1 of the exterior square L-function L(s, π,Λ2) in terms of the Shalika model on π.