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Hyperbolic uniformizations throught computations on ternary quadratic forms

Author
Alsina, M.
Type of activity
Presentation of work at congresses
Name of edition
19th Applications of Computer Algebra
Date of publication
2013
Presentation's date
2013-07-04
Book of congress proceedings
Proceedings of Applications of Computer Algebra
First page
203
Last page
206
Repository
http://hdl.handle.net/2117/20458 Open in new window
URL
http://www.aca2013.uma.es/Proceedings.pdf Open in new window
Abstract
Orders in indefinite quaternion algebras provide Fuchsian groups acting on the Poincare half-plane, used to construct the associated Shimura curves. We explain how, by using embedding theory, the elements of those Fuchsian groups depend on representations of integers by suitable ternary quadratic forms. Thus the explicit computa- tion of those representations leads to explicit presentations and fundamental domains of those Fuchsian groups, the computation of CM points, and a rich interpretation ...
Citation
Alsina, M. Hyperbolic uniformizations throught computations on ternary quadratic forms. A: Applications of Computer Algebra. "Proceedings of Applications of Computer Algebra. ACA 2013. Ed.: José Luis Galán, Gabriel Aguilera and Pedro Rodríguez". Málaga: 2013, p. 203-206.
Keywords
embeddings, fuchsian groups, quadratic forms, quaternion algebras
Group of research
TN - Number Theory Research Group

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