Quadratic unipotent Arthur parameters and residual spectrum of Sp2n

Abstract. The purpose of this paper is to study certain quadratic unipotent Arthur parameters in the sense of Moeglin and use them to parametrize a part of the residual spectrum of symplectic groups over number fields, coming from the conjugacy class of Borel subgroups. In particular, using certain identities satisfied by local intertwining operators, Arthur’s multiplicity formula is established for them which remarkably enough appears by itself in the corresponding residue of the Eisenstein series. Introduction. In this paper we study certain quadratic unipotent Arthur parameters in the sense of Moeglin [23] (cf. Section 3) and realize them as Arthur parameters [1, 2] for certain square integrable residues of Eisenstein series attached to the conjugacy class of Borel subgroups of a symplectic group over a number field. Consequently, using certain local identities proved in [11], w