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- Quaternion Orders, Quadratic Forms and Shimura Curves
Quaternion Orders, Quadratic Forms and Shimura Curves
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Shimura curves are a far-reaching generalisation of the classical modular curves. They lie at the crossroads of many areas, including complex analysis, hyperbolic geometry, algebraic geometry, algebra, and arithmetic. This monograph presents Shimura curves from a theoretical and algorithmic perspective. The main topics are Shimura curves defined over the rational number field, the construction of their fundamental domains, and the determination of their complex multiplication points.
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