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Article

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Published version

Publication date

2007

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Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/132423

Uniformization of triangle modular curves

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https://doi.org/10.5565/PUBLMAT_PJTN05_03

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.

Subject

Funcions automòrfiques, Teoria de grups

Subject (English)

Automorphic functions, Group theory

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Articles publicats en revistes (Matemàtiques i Informàtica)

Citation

BAYER I ISANT, Pilar and TRAVESA I GRAU, Artur. Uniformization of triangle modular curves. Publicacions Matemàtiques. 2007. Vol. Extra volume, num. 43-106. ISSN 0214-1493. [consulted: 12 of August of 2026]. Available at: https://hdl.handle.net/2445/132423

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