Geodesic
Elliptic Zeta Functions and Equivariant Functions
Canadian mathematical bulletin, Tome 61 (2018) no. 2, pp. 376-389

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

In this paper we establish a close connection between three notions attached to a modular subgroup, namely, the set of weight two meromorphic modular forms, the set of equivariant functions on the upper half-plane commuting with the action of the modular subgroup, and the set of elliptic zeta functions generalizing the Weierstrass zeta functions. In particular, we show that the equivariant functions can be parameterized by modular objects as well as by elliptic objects.
DOI : 10.4153/CMB-2017-034-7
Mots-clés : 11F12, 35Q15, 32L10, modular form, equivariant function, elliptic zeta function 
Sebbar, Abdellah; Al-Shbeil, Isra. Elliptic Zeta Functions and Equivariant Functions. Canadian mathematical bulletin, Tome 61 (2018) no. 2, pp. 376-389. doi: 10.4153/CMB-2017-034-7
@article{10_4153_CMB_2017_034_7,
     author = {Sebbar, Abdellah and Al-Shbeil, Isra},
     title = {Elliptic {Zeta} {Functions} and {Equivariant} {Functions}},
     journal = {Canadian mathematical bulletin},
     pages = {376--389},
     year = {2018},
     volume = {61},
     number = {2},
     doi = {10.4153/CMB-2017-034-7},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2017-034-7/}
}
TY  - JOUR
AU  - Sebbar, Abdellah
AU  - Al-Shbeil, Isra
TI  - Elliptic Zeta Functions and Equivariant Functions
JO  - Canadian mathematical bulletin
PY  - 2018
SP  - 376
EP  - 389
VL  - 61
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2017-034-7/
DO  - 10.4153/CMB-2017-034-7
ID  - 10_4153_CMB_2017_034_7
ER  - 
%0 Journal Article
%A Sebbar, Abdellah
%A Al-Shbeil, Isra
%T Elliptic Zeta Functions and Equivariant Functions
%J Canadian mathematical bulletin
%D 2018
%P 376-389
%V 61
%N 2
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-2017-034-7/
%R 10.4153/CMB-2017-034-7
%F 10_4153_CMB_2017_034_7

[1] [1] Brady, M. M., Meromorphic Solutions ofa System offunctional equations involving the modular group. Proc. Amer. Math. Soc. 30 (1971), 271–277. http://dx.doi.org/10.1090/S0002-9939-1971-0280712-5 Google Scholar

[2] [2] Conway, J. H., Understandinggroups like To(N). In: Groups, difference sets, and the Monster (Columbus, OH, 1993), Ohio State Univ. Math. Res. Inst. Publ., 4, de Gruyter, Berlin, 1996, pp. 327–343. Google Scholar

[3] [3] Elbasraoui, A. and Sebbar, A., Equivariant forms: structure and geometry. Canad. Math. Bull. 56 (2013), no. 3, 520–533. http://dx.doi.Org/10.4153/CMB-2O11-195-2 Google Scholar

[4] [4] Elbasraoui, A. and Sebbar, A., Rational equivariant forms. Int. J. Number Theory 8 (2012), no. 4, 963–981. http://dx.doi.Org/10.1142/S1 793042112500571 Google Scholar

[5] [5] Lang, S., Elliptic functions. Second ed., Graduate Texts in Mathematics, 112, Springer-Verlag, New York, 1987. http://dx.doi.org/10.1007/978-1-4612-4752-4 Google Scholar

[6] [6] Saber, H. and Sebbar, A., On the critical points of modular forms. J. Number Theory 132 (2012), no. 8, 1780–1787. http://dx.doi.Org/10.1016/j.jnt.2012.03.004 Google Scholar

[7] [7] Saber, H. and Sebbar, A., Equivariant functions and vector-valued modular forms. Int. J. Number Theory 10 (2014), no. 4, 949–954. http://dx.doi.Org/10.1142/S1793042114500092 Google Scholar

[8] [8] Sebbar, A. and Sebbar, A., Equivariant functions and integrals of elliptic functions. Geom. Dedicata 160 (2012), 373–414. http://dx.doi.Org/10.1007/s10711-011-9688-7 Google Scholar

[9] [9] Shimura, G., Introduction to the arithmetic theory of automorphic functions. Kan Memorial Lectures, 1, Publications of the Mathematical Society of Japan, 11, Iwanami Shoten, Publishers, Tokyo; Princeton University Press, Princeton, NJ, 1971. Google Scholar

[10] [10] Tannery, J. and Molk, J., Elements de la theorie des fonctions elliptiques. Gauthier-Villars, Paris, 1990. Google Scholar

Cité par Sources :