Some local-global non-vanishing results of theta lifts for symplectic-orthogonal dual pairs

Details Some local-global non-vanishing results of theta lifts for symplectic-orthogonal dual pairs Some local-global non-vanishing results of theta lifts for symplectic-orthogonal dual pairs

2008-10-16

arxiv.org/abs/0810.2990v2

Mathematics

Number Theory

Scientific paper

Following the approach of B. Roberts, we characterize the non-vanishing of global theta lifts for symplectic-orthogonal dual pairs in terms of its local counterpart. In particular, we replace the temperedness assumption present in Robert's work by a certain weaker assumption, and apply our results to small rank similitude groups. Among our applications is a certain instance of Langlands functorial transfer of a (non-generic) cuspidal automorphic representation of $GSp(4)$ to GL(4).

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