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The residual spectrum of Sp 4 . (English) Zbl 0877.11030
In this paper the author uses Langlands’ method to analyze the residual spectrum of the group Sp 4 over a number field. According to Langlands’ general principles there is a decomposition corresponding to the classes of parabolic subgroups. In the case of the Siegel parabolic subgroup the author obtains a decomposition depending on cuspidal representations of GL 2 with trivial central characters satisfying, essentially, L(1/2,π)0. In the case of the other two maximal parabolic subgroups he obtains a decomposition parametrized by monomial representations of GL 2 . In the case of the Borel subgroup the decomposition is parametrized by Größencharaktere of order 2, but the irreducible representations are selected by a parity condition on the ε-factors and so do not correspond to the entire global L-packet.

MSC:
11F70Representation-theoretic methods in automorphic theory
11F67Special values of automorphic L-series, etc