Computing Power Series Expansions of Modular Forms

Part of the Contributions in Mathematical and Computational Sciences book series (CMCS, volume 6)

Abstract

We exhibit a method to numerically compute power series expansions of modular forms on a cocompact Fuchsian group, using the explicit computation of a fundamental domain and linear algebra. As applications, we compute Shimura curve parametrizations of elliptic curves over a totally real field, including the image of CM points, and equations for Shimura curves.

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsUniversity of VermontBurlingtonUSA
  2. 2.Department of MathematicsDartmouth CollegeHanoverUSA
  3. 3.Department of MathematicsThe University of Colorado at BoulderBoulderUSA

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