Schwarzian differential equations and Hecke eigenforms on Shimura curves

Abstract

Let $X$ be a Shimura curve of genus zero. In this paper, we first characterize the spaces of automorphic forms on $X$ in terms of Schwarzian differential equations. We then devise a method to compute Hecke operators on these spaces. An interesting by-product of our analysis is the evaluation $${}_2{F}_1(1/24,7/24,5/6,-\frac{2^{10}\cdot 3^3\cdot 5}{11^4})=\sqrt{6}\sqrt[6]{\frac{11}{5^5}}$$ and other similar identities.

31 pages, 2 figures

References in corpus (1)

• Modular forms of half-integral weights on SL(2,Z)

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