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Hyperbolic uniformizations throught computations on ternary quadratic forms
Alsina Aubach, Montserrat
Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada III; Universitat Politècnica de Catalunya. TN - Teoria de Nombres
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 computation of those representations leads to explicit presentations and fundamental domains of those Fuchsian groups, the computation of CM points, and a rich interpretation of the points in the complex upper half-plane.
Peer Reviewed
Àrees temàtiques de la UPC::Matemàtiques i estadística
Fuchsian groups
Embeddings (Mathematics)
Forms, Quadratic
Quaternions
Fuchsian groups, quaternion algebras, quadratic forms, embeddings
Fuchsian, Grups de
Formes quadràtiques
Quaternions
Attribution 3.0 Spain
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