Distinguished residual spectrum for GL2(D)

Mahendra Kumar Verma

Research output: Contribution to journalArticlepeer-review


Let G D GL2(D) where D is a quaternion division algebra over a number field F and H D Sp2(D) is the unique inner form of Sp4(F). We study the period of an automorphic form on G(A[double-struck]) relative to H(A[double-struck]) 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.

Original languageEnglish
Pages (from-to)241-256
Number of pages16
JournalPacific Journal of Mathematics
Issue number1
StatePublished - 1 Jan 2018


  • Jacquet-Langlands correspondence
  • Symplectic period

ASJC Scopus subject areas

  • General Mathematics


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