Functiones et Approximatio Commentarii Mathematici

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

Cristian Virdol

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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.

Article information

Funct. Approx. Comment. Math., Volume 49, Number 2 (2013), 221-227.

First available in Project Euclid: 20 December 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 11F41: Automorphic forms on GL(2); Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces [See also 14J20]
Secondary: 11F80: Galois representations 11R42: Zeta functions and $L$-functions of number fields [See also 11M41, 19F27] 11R80: Totally real fields [See also 12J15]

critical values CM-fields Hilbert modular forms


Virdol, Cristian. The critical values of $L$-functions of CM-base change for Hilbert modular forms. Funct. Approx. Comment. Math. 49 (2013), no. 2, 221--227. doi:10.7169/facm/2013.49.2.2.

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