On the hyperbolic uniformization of Shimura curves with an Atkin-Lehner quotient of genus 0

[eng] The main goal of this thesis is to contribute to the explicit hyperbolic uniformization of Shimura curves. We will restrict to the case of curves attached to Eichler orders in rational quaternion algebras whose maximal Atkin-Lehner quotient has genus 0, which despite multiple differences bears...

Descripción completa

Detalles Bibliográficos
Autor: Nualart Riera, Joan
Tipo de recurso: tesis doctoral
Estado:Versión publicada
Fecha de publicación:2016
País:España
Institución:Universidad de Barcelona
Repositorio:Dipòsit Digital de la UB
OAI Identifier:oai:diposit.ub.edu:2445/102688
Acceso en línea:https://hdl.handle.net/2445/102688
http://hdl.handle.net/10803/396134
Access Level:acceso abierto
Palabra clave:Funcions automòrfiques
Formes automòrfiques
Corbes
Varietats de Shimura
Invariants
Superfícies de Riemann
Automorphic functions
Automorphic forms
Curves
Shimura varieties
Riemann surfaces
Descripción
Sumario:[eng] The main goal of this thesis is to contribute to the explicit hyperbolic uniformization of Shimura curves. We will restrict to the case of curves attached to Eichler orders in rational quaternion algebras whose maximal Atkin-Lehner quotient has genus 0, which despite multiple differences bears some resemblance to the classical modular case. We will provide an approach to obtain an explicit uniformization of these curves and some of their covers, together with several applications. We will illustrate all the applications with plenty of examples.