The Belyi Characterization of a Class of Modular Curves
Journal de Théorie des Nombres de Bordeaux, Tome 30 (2018) no. 2, pp. 409-429.

Une classe de courbes modulaires est caractérisée par l’existence de certains couples de fonctions de Belyi qui engendrent leurs corps des fonctions. Des applications à l’équation modulaire et au calcul de valeurs spéciales de la fonction j sont données.

A class of modular curves is characterized by the existence of certain pairs of Belyi functions which generate their function fields. Applications to the modular equation and the computation of special values of the j-function are given.

Reçu le :
Révisé le :
Accepté le :
Publié le :
DOI : https://doi.org/10.5802/jtnb.1031
Classification : 14H57,  11F03,  14Q05
Mots clés : dessins d’enfants, Belyi functions, modular curves, modular equation
@article{JTNB_2018__30_2_409_0,
     author = {Khashayar Filom},
     title = {The {Belyi} {Characterization} of a {Class} of {Modular} {Curves}},
     journal = {Journal de Th\'eorie des Nombres de Bordeaux},
     pages = {409--429},
     publisher = {Soci\'et\'e Arithm\'etique de Bordeaux},
     volume = {30},
     number = {2},
     year = {2018},
     doi = {10.5802/jtnb.1031},
     language = {en},
     url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1031/}
}
TY  - JOUR
AU  - Khashayar Filom
TI  - The Belyi Characterization of a Class of Modular Curves
JO  - Journal de Théorie des Nombres de Bordeaux
PY  - 2018
DA  - 2018///
SP  - 409
EP  - 429
VL  - 30
IS  - 2
PB  - Société Arithmétique de Bordeaux
UR  - https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1031/
UR  - https://doi.org/10.5802/jtnb.1031
DO  - 10.5802/jtnb.1031
LA  - en
ID  - JTNB_2018__30_2_409_0
ER  - 
Khashayar Filom. The Belyi Characterization of a Class of Modular Curves. Journal de Théorie des Nombres de Bordeaux, Tome 30 (2018) no. 2, pp. 409-429. doi : 10.5802/jtnb.1031. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1031/

[1] Khashayar Filom; Ali Kamalinejad Dessins on Modular Curves (2016) (https://arxiv.org/abs/1603.01693)

[2] Ernesto Girondo; Gabino Gonzàlez-Diez Introduction to Compact Riemann Surfaces and Dessins d’Enfants, London Mathematical Society Student Texts, Volume 79, Cambridge University Press, 2012, xii+298 pages | Zbl 1253.30001

[3] Yang-Hui He; John McKay; James Read Modular subgroups, dessins d’enfants and elliptic K3 surfaces, LMS J. Comput. Math., Volume 16 (2013), pp. 271-318 | Zbl 1298.11058

[4] Sergei K. Lando; Alexander K. Zvonkin Graphs on Surfaces and Their Applications, Encyclopaedia of Mathematical Sciences, Volume 141, Springer, 2004, xv+455 pages | Zbl 1040.05001

[5] John McKay; Abdellah Sebbar J-invariants of arithmetic semistable elliptic surfaces and graphs, Proceedings on Moonshine and related topics (Montréal, 1999) (CRM Proceedings & Lecture Notes) Volume 30, American Mathematical Society, 2001, pp. 119-130 | Zbl 1191.11010

[6] James Stuart Milne Modular Functions and Modular Forms (Elliptic Modular Curves) (2012) (http://www.jmilne.org/math/CourseNotes/MF.pdf)

[7] Jeroen Sijsling; John Michael Voight On computing Belyi maps, Publ. Math. Besançon, Algèbre Théor. Nombres, Volume 2014 (2014) no. 1, pp. 73-131 | Zbl 1364.11127

Cité par Sources :