Computing Hilbert modular forms over real quadratic fields

Опубликовано 6 сентября 2016, 6:34

I will present an algorithm which computes Hilbert modular forms on real quadratic fields. The computations exploit the Jacquet-Langlands correspondence to switch to definite quaternions algebras and are intimately related to the computations of the class numbers of the latter. We will illustrate our discussion with several examples.