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The residual spectrum of $Sp\sb 4$. (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, $L(1/2,\pi) \ne 0$. 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 $\varepsilon$-factors and so do not correspond to the entire global $L$-packet.

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