Abstract
In this paper, we extend the results on G2-period of residual representations of SO8 in [Jng98a], [Jng98b] to a generalized G2-period of residual representations of SO2l (l≥4). The period is expected to detect the nonvanishing of the relevant tensor product L-function at the center of the symmetry, which is a special case of the Gross- Prasad conjecture. More general cases will be considered in our forth-coming work [GJRa], [GJRb].
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