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

Abstract

In this paper we generalize some results, obtained by Shimura, on the critical values of $L$-functions of $l$-adic representations attached to quadratic CM-base change of Hilbert modular forms twisted by finite order characters, to the case of the critical values of $L$-functions of arbitrary base change to CM-number fields of $l$-adic representations attached to Hilbert modular forms twisted by some finite-dimensional representations.