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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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.

Article information

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

Dates
First available in Project Euclid: 20 December 2013

Permanent link to this document
https://projecteuclid.org/euclid.facm/1387572227

Digital Object Identifier
doi:10.7169/facm/2013.49.2.2

Mathematical Reviews number (MathSciNet)
MR2987107

Zentralblatt MATH identifier
1297.11032

Subjects
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]

Keywords
critical values CM-fields Hilbert modular forms

Citation

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. https://projecteuclid.org/euclid.facm/1387572227


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References

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