The critical values of $L$-functions of base change for Hilbert modular forms

Abstract

In this paper we generalize some results, obtained by Shimura, Yoshida and the author, on critical values of $L$-functions of $l$-adic representations attached to Hilbert modular forms twisted by finite order characters, 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 twisted by some general finite-dimensional representations.