Vector-Valued Modular Forms of Weight Two Associated With Jacobi-Like Forms
Canadian mathematical bulletin, Tome 49 (2006) no. 3, pp. 428-437

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

We construct vector-valued modular forms of weight 2 associated to Jacobi-like forms with respect to a symmetric tensor representation of $\Gamma$ by using the method of Kuga and Shimura as well as the correspondence between Jacobi-like forms and sequences of modular forms. As an application, we obtain vector-valued modular forms determined by theta functions and by pseudodifferential operators.
DOI : 10.4153/CMB-2006-042-2
Mots-clés : 11F11, 11F50
Lee, Min Ho. Vector-Valued Modular Forms of Weight Two Associated With Jacobi-Like Forms. Canadian mathematical bulletin, Tome 49 (2006) no. 3, pp. 428-437. doi: 10.4153/CMB-2006-042-2
@article{10_4153_CMB_2006_042_2,
     author = {Lee, Min Ho},
     title = {Vector-Valued {Modular} {Forms} of {Weight} {Two} {Associated} {With} {Jacobi-Like} {Forms}},
     journal = {Canadian mathematical bulletin},
     pages = {428--437},
     year = {2006},
     volume = {49},
     number = {3},
     doi = {10.4153/CMB-2006-042-2},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2006-042-2/}
}
TY  - JOUR
AU  - Lee, Min Ho
TI  - Vector-Valued Modular Forms of Weight Two Associated With Jacobi-Like Forms
JO  - Canadian mathematical bulletin
PY  - 2006
SP  - 428
EP  - 437
VL  - 49
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2006-042-2/
DO  - 10.4153/CMB-2006-042-2
ID  - 10_4153_CMB_2006_042_2
ER  - 
%0 Journal Article
%A Lee, Min Ho
%T Vector-Valued Modular Forms of Weight Two Associated With Jacobi-Like Forms
%J Canadian mathematical bulletin
%D 2006
%P 428-437
%V 49
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-2006-042-2/
%R 10.4153/CMB-2006-042-2
%F 10_4153_CMB_2006_042_2

[1] [1] Cohen, P., Manin, Y., and Zagier, D., Automorphic pseudodifferential operators. In: Algebraic Aspects of Nonlinear Systems, Progr. Nonlinear Differential Equations Appl. 26, Birkhäuser, Boston, 1997, pp. 17–47. Google Scholar

[2] [2] Dong, C. and Mason, G., Transformation laws for theta functions. In: Proceedings onMoonshine and Related Topics, CRM Proc. Lecture Notes 30, American Mathematical Society, Providence, RI, 2001, pp. 15–26. Google Scholar

[3] [3] Eichler, M., Eine Verallgemeinerung der Abelschen Integrals. Math. Z. 67(1957), 267–298. Google Scholar

[4] [4] Eichler, M. and Zagier, D., The Theory of Jacobi Forms, Progress in Mathematics 55, Birkhäuser, Boston, 1985. Google Scholar

[5] [5] Kuga, M. and Shimura, G., On vector differential forms attached to automorphic forms. J. Math. Soc. Japan 12(1960), 258–270. Google Scholar

[6] [6] Lee, M. H., Modular forms associated to theta functions. Canad. Math. Bull. 45(2002), no. 2, 257–264. Google Scholar

[7] [7] Shimura, G., Sur les intégrales attachées aux formes automorphes. J. Math. Soc. Japan 11(1959), 291–311. Google Scholar

[8] [8] Zagier, D., Modular forms and differential operators. Proc. Indian Acad. Sci. Math. Sci. 104(1994), no. 1, 57–75. Google Scholar

Cité par Sources :