ON SPECIAL VALUES OF CERTAIN L-FUNCTIONS, II

We prove an algebraicity result concerning special values at critical points, in the sense of Deligne, of tensor product L-functions associated to automorphic representations of special orthogonal groups for quadratic forms which are totally definite, and, cuspidal representations of GL(2) corresponding to primitive cusp forms, over totally real number fields. We also prove the reciprocity law, i.e., the equivariance under the action of Gal(ℚ̅/ℚ), for the special values. In the appendix, the second author calculates the Deligne periods for such L-functions, assuming the existence of corresponding motives and the automorphic transfer to a quasi-split form of the special orthogonal group. Our result conforms with the celebrated conjecture of Deligne on special values of motivic L-functions.