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.
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