On the adjoint \(L\)-function of the \(p\)-adic \(\text{GSp}(4)\). (English) Zbl 1213.11110
Summary: We explicitly compute the adjoint \(L\)-function of those \(L\)-packets of representations of the group \(\text{GSp}(4)\) over a \(p\)-adic field of characteristic zero that contain non-supercuspidal representations. As an application we verify a conjecture of Gross and Prasad and Rallis in this case. The conjecture states that the adjoint \(L\)-function is holomorphic at \(s=1\) if and only if the \(L\)-packet contains a generic representation.
MSC:
| 11F70 | Representation-theoretic methods; automorphic representations over local and global fields |
| 11F66 | Langlands \(L\)-functions; one variable Dirichlet series and functional equations |
| 11F67 | Special values of automorphic \(L\)-series, periods of automorphic forms, cohomology, modular symbols |
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