Explicit methods for Hilbert modular forms
Lassina Dembele, John Voight
TL;DR
This paper presents algorithms for computing Hecke eigenvalues of Hilbert modular forms over totally real fields, with explicit examples and applications to modularity and Galois representations.
Contribution
It introduces new algorithms for computing Hilbert modular forms and demonstrates their effectiveness through explicit examples and applications.
Findings
Algorithms successfully compute Hecke eigenvalues
Explicit examples illustrate the methods
Applications to modularity and Galois representations
Abstract
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.
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Taxonomy
TopicsAdvanced Algebra and Geometry · Algebraic Geometry and Number Theory · Analytic Number Theory Research