ON THE SPECIAL VALUES OF L-FUNCTIONS OF CM-BASE CHANGE FOR HILBERT MODULAR FORMS
Glasgow mathematical journal, Tome 56 (2014) no. 1, pp. 57-63

Voir la notice de l'article provenant de la source Cambridge University Press

In this paper we generalize some results, obtained by Shimura, on the special values of L-functions of l-adic representations attached to quadratic CM-base change of Hilbert modular forms twisted by finite order characters. The generalization is to the case of the special 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.
DOI : 10.1017/S0017089513000074
Mots-clés : 11F41, 11F80, 11R42, 11R80
VIRDOL, CRISTIAN. ON THE SPECIAL VALUES OF L-FUNCTIONS OF CM-BASE CHANGE FOR HILBERT MODULAR FORMS. Glasgow mathematical journal, Tome 56 (2014) no. 1, pp. 57-63. doi: 10.1017/S0017089513000074
@article{10_1017_S0017089513000074,
     author = {VIRDOL, CRISTIAN},
     title = {ON {THE} {SPECIAL} {VALUES} {OF} {L-FUNCTIONS} {OF} {CM-BASE} {CHANGE} {FOR} {HILBERT} {MODULAR} {FORMS}},
     journal = {Glasgow mathematical journal},
     pages = {57--63},
     year = {2014},
     volume = {56},
     number = {1},
     doi = {10.1017/S0017089513000074},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089513000074/}
}
TY  - JOUR
AU  - VIRDOL, CRISTIAN
TI  - ON THE SPECIAL VALUES OF L-FUNCTIONS OF CM-BASE CHANGE FOR HILBERT MODULAR FORMS
JO  - Glasgow mathematical journal
PY  - 2014
SP  - 57
EP  - 63
VL  - 56
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.1017/S0017089513000074/
DO  - 10.1017/S0017089513000074
ID  - 10_1017_S0017089513000074
ER  - 
%0 Journal Article
%A VIRDOL, CRISTIAN
%T ON THE SPECIAL VALUES OF L-FUNCTIONS OF CM-BASE CHANGE FOR HILBERT MODULAR FORMS
%J Glasgow mathematical journal
%D 2014
%P 57-63
%V 56
%N 1
%U http://geodesic.mathdoc.fr/articles/10.1017/S0017089513000074/
%R 10.1017/S0017089513000074
%F 10_1017_S0017089513000074

[1] 1.Barnet-Lamb, T., Gee, T., Geraghty, D. and Taylor, R., Potential automorphy and change of weight (preprint). arXiv:1010.2561v1 [math.NT]. Google Scholar

[2] 2.Barnet-Lamb, T., Geraghty, D., Harris, M. and Taylor, R., A family of Calabi-Yau varieties and potential automorphy II, Publ. Res. Inst. Math. Sci. 47 (2011), 29–98. Google Scholar | DOI

[3] 3.Curtis, C. W. and Reiner, I., Methods of representation theory, vol. I (Wiley, New York, NY, 1981). Google Scholar

[4] 4.Deligne, P., Valeurs de fonctions L et periodes d'integrales, Proc. Symp. Pure Math. 33 (part 2) (1979), 313–346. Google Scholar | DOI

[5] 5.Langlands, R. P., Base change for GL(2), Ann. of Mathematics Studies, No. 96 (Princeton University Press, Princeton, NJ, 1980). Google Scholar

[6] 6.Shimura, G., The special values of the zeta functions associated with Hilbert modular forms, Duke Math. J. 45 (1978), 637–679. Google Scholar

[7] 7.Shimura, G., Algebraic relations between critical values of zeta functions and inner products, Amer. J. Math. 104 (1983), 253–285. Google Scholar

[8] 8.Taylor, R., On Galois representations associated to Hilbert modular forms, Invent. Math. 98 (1989), 265–280. Google Scholar | DOI

[9] 9.Virdol, C., Tate classes and poles of L-functions of twisted quaternionic Shimura surfaces, J. Number Theory 123 (2) (2007), 315–328. Google Scholar | DOI

[10] 10.Virdol, C., On the critical values of L-functions of tensor product of base change for Hilbert modular forms, J. Math. Kyoto Univ. 49 (2) (2009), 347–357. Google Scholar

[11] 11.Virdol, C., On the critical values of L-functions of base change for Hilbert modular forms, Amer. J. Math. 132 (4) (2010), 1105–1111. Google Scholar | DOI

[12] 12.Virdol, C., Non-solvable base change for Hilbert modular forms and zeta functions of twisted quaternionic Shimura varieties, Annales de la Faculte des Sciences de Toulouse 19 (3–4) (2010), 831–848. Google Scholar

[13] 13.Virdol, C., On the Birch and Swinnerton-Dyer conjecture for abelian varieties attached to Hilbert modular forms, J. Number Theory 131 (4) (2011), 681–684. Google Scholar | DOI

Cité par Sources :