The Ramanujan Journal

, Volume 12, Issue 2, pp 207–223

Hyperbolic uniformization of Fermat curves


DOI: 10.1007/s11139-006-0074-2

Cite this article as:
Bayer, P. & Guàrdia, J. Ramanujan J (2006) 12: 207. doi:10.1007/s11139-006-0074-2


The ground-breaking research on the uniformization of curves was conducted at the beginning of the last century. Nevertheless, there are few examples in the literature of algebraic curves for which an explicit uniformization is known. In this article we obtain an explicit uniformization of the Fermat curves FN, for each \(N\geq 4\). The results presented here are based in part on an earlier study of the second author [6] in which each Riemann surface FN() was described as a quotient of the complex disk by a Fuchsian group Γ.


Hyperbolic uniformization Fundamental domains Fermat curves 

Copyright information

© Springer Science + Business Media, LLC 2006

Authors and Affiliations

  1. 1.Facultat de MatemàtiquesUniversitat de BarcelonaBarcelonaSpain
  2. 2.Departament de Matemàtica Aplicada IVEscola Politècnica Superior d’Enginyeria de Vilanova i la GeltrúVilanova i la GeltrúSpain

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