Hokkaido Mathematical Journal

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

Cristian VIRDOL

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Abstract

In this paper we generalize some results, obtained by Shimura, Yoshida and the author, 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.

Article information

Source
Hokkaido Math. J., Volume 48, Number 2 (2019), 245-252.

Dates
First available in Project Euclid: 11 July 2019

Permanent link to this document
https://projecteuclid.org/euclid.hokmj/1562810506

Digital Object Identifier
doi:10.14492/hokmj/1562810506

Mathematical Reviews number (MathSciNet)
MR3980940

Zentralblatt MATH identifier
07080092

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] 11F80: Galois representations 11R42: Zeta functions and $L$-functions of number fields [See also 11M41, 19F27] 11R80: Totally real fields [See also 12J15]

Keywords
$L$-functions special values Hilbert modular forms

Citation

VIRDOL, Cristian. The critical values of $L$-functions of base change for Hilbert modular forms. Hokkaido Math. J. 48 (2019), no. 2, 245--252. doi:10.14492/hokmj/1562810506. https://projecteuclid.org/euclid.hokmj/1562810506


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