Abstract
We study the Schwarz triangle function with the monodromy group $\Delta(7,7,7)$, and we construct its inverse by theta constants. As consequences, we give uniformizations of the Klein quartic curve and the Fermat septic curve as Shimura curves parametrizing Abelian $6$-folds with endomorphisms $\mathbb{Z}[\zeta_7]$.
Citation
Kenji KOIKE. "The Fermat septic and the Klein quartic as moduli spaces of hypergeometric Jacobians." Hokkaido Math. J. 47 (1) 109 - 141, February 2018. https://doi.org/10.14492/hokmj/1520928062
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