English

Computing automorphic forms on Shimura curves over fields with arbitrary class number

Number Theory 2015-03-17 v1

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

Cite

@article{arxiv.1004.5340,
  title  = {Computing automorphic forms on Shimura curves over fields with arbitrary class number},
  author = {John Voight},
  journal= {arXiv preprint arXiv:1004.5340},
  year   = {2015}
}

Comments

15 pages; final submission to ANTS IX

R2 v1 2026-06-21T15:16:34.511Z