Automorphy factors for a Hilbert modular group

The Scattering Matrix for the Hilbert Modular Group

In this paper, we compute the scattering matrix for the Hilbert modular group over any number field K. We then express the determinant of the scattering matrix as a ratio of completed Dedekind zeta functions associated to the Hilbert class field of K. This generalizes work of Efrat and Sarnak [ES] in the imaginary quadratic case.

A computational approach to Hilbert modular group fixed points

Some useful information is known about the fundamental domain for certain Hilbert modular groups. The six nonequivalent points with nontrivial isotropy in the fundamental domains under the action of the modular group for Q( √ 5), Q( √ 2), and Q( √ 3) have been determined previously by Gundlach. In finding these points, use was made of the exact size of the isotropy groups. Here we show that the...

Tate Conjectures for Hilbert Modular Surfaces

Explicit Methods for Hilbert Modular Forms

We exhibit algorithms to compute systems of Hecke eigenvalues for spaces of Hilbert modular forms over a totally real field. We provide many explicit examples as well as applications to modularity and Galois representations.

On Ihara’s lemma for Hilbert Modular Varieties

Let ρ be a modulo p representation of the absolute Galois group of a totally real number field. Under the assumptions that ρ has large image and admits a low weight crystalline modular deformation we show that any low weight crystalline deformation of ρ unramified outside a finite set of primes will be modular. We follow the approach of Wiles as generalized by Fujiwara. The main new ingredient ...