CM-points and Lattice counting on arithmetic compact Riemann surfaces

Let $X(D,1) =\Gamma(D,1) \backslash \mathbb{H}$ denote the Shimura curve of level $N=1$ arising from an indefinite quaternion algebra of fixed discriminant $D$. We study the discrete average of the error term in the hyperbolic circle problem over Heegner points of discriminant $d <0$ on $X(D,1)$ as $d \to -\infty$. We prove that if $|d|$ is sufficiently large compared to the radius $r \approx \log X$ of the circle, we can improve on the classical $O(X^{2/3})$-bound of Selberg. Our result extends the result of Petridis and Risager for the modular surface to arithmetic compact Riemann surfaces.Comment: 10 pages; Final version to appear in Journal of Number Theor

El projecte 7demates

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Col·lecció Congressos-1: VSST 2007 Vieille Stratégique, Scientifique et Technologique

Ressenya de les VSST 2007: Journées de Veille Stratégique, Scientifique et Technologique que van tenir lloc del 21 al 25 d'Octubre de 2007 a Marrakech, organitzades per l'Universitat Politècnica de Catalunya, l'Institut de Recherche en Information de Toulouse i la Société Française de Bibliométrie Appliquée. Review of the VSST 2007: Journées de Veille Stratégique, Scientifique et Technologique that took place from 21th till the 25th of October, 2007, in Marrakech. The sessions were organized by the Universitat Politècnica de Catalunya, the Institut de Recherche en Information de Toulouse and the Société Française de Bibliométrie Appliquée

Entrevista a Nuno Freitas, Premio José Luis Rubio de Francia 2014

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Exposició "Les matemàtiques i la vida"

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Ciencia en Acción 2014

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Hyperbolic uniformizations throught computations on ternary quadratic forms

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 ReviewedPostprint (published version

Colección Congresos-1: VSST 2007 Vieille Stratégique, Scientifique et Technologique

Reseña del congreso "Vieille Stratégique, Scientifique et Technologique