Vol. 295, No. 1, 2018

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Distinguished residual spectrum for $\mathop{\rm GL}_2(D)$

Mahendra Kumar Verma

Vol. 295 (2018), No. 1, 241–256

Let G = GL2(D) where D is a quaternion division algebra over a number field F and H = Sp2(D) is the unique inner form of Sp4(F). We study the period of an automorphic form on G(A) relative to H(A) and we provide a formula, similar to the split case, for an automorphic form in the residual spectrum. We confirm the conjecture due to Dipendra Prasad for noncuspidal automorphic representations, which says that symplectic period is preserved under the global Jacquet–Langlands correspondence.

symplectic period, Jacquet–Langlands correspondence
Mathematical Subject Classification 2010
Primary: 11F41, 11F67, 11F70
Received: 31 August 2017
Revised: 5 December 2017
Accepted: 15 December 2017
Published: 13 March 2018
Mahendra Kumar Verma
Department of Mathematics
Ben-Gurion University of Negev