On the critical values of $L$-functions of tensor product of base change for Hilbert modular forms

In this paper we generalize some results, obtained by Shimura, Yoshida on critical values of L-functions of l-adic representations attached to tensor product of Hilbert modular forms, to the critical values of L-functions of arbitrary base change to totally real number elds of l-adic representations attached to tensor product of Hilbert modular forms.