The critical values of \(L\)-functions of CM-base change for Hilbert modular forms (Q2637417)

In this paper the author generalized \textit{G. Shimura}'s results [Duke Math. J. 45, 637--679 (1978; Zbl 0394.10015); Am. J. Math. 105, 253--285 (1983; Zbl 0518.10032)] on the critical values of \(L\)-functions of \(\ell\)-adic representations attached to quadratic CM-base change of Hilbert modular forms twisted by finite order characters. Analogous results on the critical values of \(L\)-functions of arbitrary base change to CM-number fields of \(\ell\)-adic representations attached to Hilbert modular forms twisted by some finite-dimensional representations were established.