Abstract
This paper deals with Deligne's conjecture on the critical values of L-functions. Let Z G ⊗ h (s) denote the tensor product L-function attached to a Siegel modular form G of weight k and an elliptic cusp form h of weight l. We assume that the first Fourier-Jacobi coefficient of G is not identically zero. Then Deligne's conjecture is fully proven for Z G ⊗ h (s), when l≤2k−2 and partly for the remaining case.
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