Uniformization of triangle modular curves.

Bayer, Pilar, and Travesa, Artur. "Uniformization of triangle modular curves.." Publicacions Matemàtiques 51.Extra (2007): 43-106. <http://eudml.org/doc/41915>.

@article{Bayer2007,
abstract = {In the present article, we determine explicit uniformizations of modular curves attached to triangle Fuchsian groups with cusps. Their Hauptmoduln are obtained by integration of non-linear differential equations of the third order. Series expansions involving integral coefficients are calculated around the cusps as well as around the elliptic points. The method is an updated form of a differential construction of the elliptic modular function j, first performed by Dedekind in 1877. Subtle differences between automorphic functions with respect to conjugate Fuchsian groups become apparent.[Proceedings of the Primeras Jornadas de Teoría de Números (Vilanova i la Geltrú (Barcelona), 30 June - 2 July 2005)].},
author = {Bayer, Pilar, Travesa, Artur},
journal = {Publicacions Matemàtiques},
keywords = {Teoría de números; Grupos fuchsianos; Funciones modulares; arithmetical Fuchsian group; triangle groups; Fuchsian differential equations; Schwarzian derivative; modular curve},
language = {eng},
number = {Extra},
pages = {43-106},
title = {Uniformization of triangle modular curves.},
url = {http://eudml.org/doc/41915},
volume = {51},
year = {2007},
}

TY - JOUR
AU - Bayer, Pilar
AU - Travesa, Artur
TI - Uniformization of triangle modular curves.
JO - Publicacions Matemàtiques
PY - 2007
VL - 51
IS - Extra
SP - 43
EP - 106
AB - In the present article, we determine explicit uniformizations of modular curves attached to triangle Fuchsian groups with cusps. Their Hauptmoduln are obtained by integration of non-linear differential equations of the third order. Series expansions involving integral coefficients are calculated around the cusps as well as around the elliptic points. The method is an updated form of a differential construction of the elliptic modular function j, first performed by Dedekind in 1877. Subtle differences between automorphic functions with respect to conjugate Fuchsian groups become apparent.[Proceedings of the Primeras Jornadas de Teoría de Números (Vilanova i la Geltrú (Barcelona), 30 June - 2 July 2005)].
LA - eng
KW - Teoría de números; Grupos fuchsianos; Funciones modulares; arithmetical Fuchsian group; triangle groups; Fuchsian differential equations; Schwarzian derivative; modular curve
UR - http://eudml.org/doc/41915
ER -