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The residual spectrum of $S{p}_{4}$. (English) Zbl 0877.11030
In this paper the author uses Langlands’ method to analyze the residual spectrum of the group $S{p}_{4}$ 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 $G{L}_{2}$ with trivial central characters satisfying, essentially, $L\left(1/2,\pi \right)\ne 0$. In the case of the other two maximal parabolic subgroups he obtains a decomposition parametrized by monomial representations of $G{L}_{2}$. 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 $\epsilon$-factors and so do not correspond to the entire global $L$-packet.

##### MSC:
 11F70 Representation-theoretic methods in automorphic theory 11F67 Special values of automorphic $L$-series, etc