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In this paper we introduce an automorphic variant of the Deligne conjecturefor tensor product of two motives over a quadratic imaginary field. On onehand, we define some motivic periods and rewrite the Deligne conjecture interms of these periods. On the other hand, we define the automorphic analogueof these motivic periods and then give a purely automorphic variant of theDeligne conjecture. At last, we introduce some known results of thisautomorphic variant.

An automorphic variant of the Deligne conjecture