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Singular Moduli of Shimura Curves

dc.contributor.advisorKudla, Stephen Sen_US
dc.contributor.authorErrthum, Eric Francisen_US
dc.description.abstractThe j-function acts as a parametrization of the classical modular curve. Its values at complex multiplication (CM) points are called singular moduli and are algebraic integers. A Shimura curve is a generalization of the modular curve and, if the Shimura curve has genus 0, a rational parameterizing function evaluated at a CM point is again algebraic over the rational field. This thesis shows that the coordinate maps given by Elkies for the Shimura curves associated to the quaternion algebras with discriminants 6 and 10 are Borcherds lifts of vector-valued modular forms. This property is then used to explicitly compute the rational norms of singular moduli on these curves. This method not only verifies the conjectural values for the rational CM points given by Elkies, but also provides a way of algebraically calculating the norms of CM points with arbitrarily large negative discriminant.en_US
dc.format.extent500477 bytes
dc.format.extent109876 bytes
dc.titleSingular Moduli of Shimura Curvesen_US
dc.contributor.publisherDigital Repository at the University of Marylanden_US
dc.contributor.publisherUniversity of Maryland (College Park, Md.)en_US
dc.subject.pquncontrolledSingular Modulien_US
dc.subject.pquncontrolledShimura Curvesen_US
dc.subject.pquncontrolledQuaternion Algebraen_US

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