BIRS Workshop Lecture Videos

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BIRS Workshop Lecture Videos

Explicit methods for Shimura curves Yang, Yifan


Shimura curves are generalisations of classical modular curves. However, because of the lack of cusps on Shimura curves, there have been very few explicit methods for Shimura curves. In this talk, we will introduce two realisations of modular forms on Shimura curves, one in terms of solutions of Schwarzian differential equations and the other in terms of Borcherds forms, and discuss their applications, including special values of hypergeometric functions, equations of (hyperelliptic) Shimura curves, and explicit description of quaternionic loci in Siegel's modular threefold.

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