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

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