Explicit methods for Hilbert modular forms

2010/10/27 by Lassina Dembélé, Dembele, Lassina, John Voight +1 · 2 citations
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1010.5727

openalex publication_date 2010/10/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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• Obstructions to unirationality for product-quotient surfaces over \mathbbF_p
• Computing Hilbert modular forms as orthogonal modular forms

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