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The critical values of \(L\)-functions of base change for Hilbert modular forms. (English) Zbl 1437.11074
Summary: In this paper we generalize some results, obtained by G. Shimura [Duke Math. J. 45, 637–679 (1978; Zbl 0394.10015)], H. Yoshida [Am. J. Math. 117, No. 4, 1019–1038 (1995; Zbl 0841.11024)] and the author [Am. J. Math. 132, No. 4, 1105–1111 (2010; Zbl 1217.11053)], 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.
MSC:
11F41 Automorphic forms on \(\mbox{GL}(2)\); Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces
11F80 Galois representations
11R42 Zeta functions and \(L\)-functions of number fields
11R80 Totally real fields
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