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Computing Automorphic Forms on Shimura Curves over Fields with Arbitrary Class Number

  • John Voight
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6197)

Abstract

We extend methods of Greenberg and the author to compute in the cohomology of a Shimura curve defined over a totally real field with arbitrary class number. Via the Jacquet-Langlands correspondence, we thereby compute systems of Hecke eigenvalues associated to Hilbert modular forms of arbitrary level over a totally real field of odd degree. We conclude with two examples which illustrate the effectiveness of our algorithms.

Keywords

Modular Form Class Number Automorphic Form Quaternion Algebra Real Place 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • John Voight
    • 1
  1. 1.Department of Mathematics and StatisticsUniversity of VermontBurlingtonUSA

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