Computing Hilbert Modular Forms over Fields with Nontrivial Class Group

DOI10.1007/978-3-540-79456-1_25zbMath1232.11128arXiv0711.3863OpenAlexW1891353357MaRDI QIDQ5387611

Lassina Dembélé, Steve Donnelly

Publication date: 27 May 2008

Published in: Lecture Notes in Computer Science (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0711.3863

Mathematics Subject Classification ID

Analysis of algorithms (68W40) Algebraic number theory computations (11Y40) Automorphic forms on (mbox{GL}(2)); Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces (11F41)

Related Items

Computation of lattice isomorphisms and the integral matrix similarity problem ⋮ Computing systems of Hecke eigenvalues associated to Hilbert modular forms ⋮ Computing ideal classes representatives in quaternion algebras ⋮ On some bounds for symmetric tensor rank of multiplication in finite fields ⋮ Canonical models of arithmetic \((1; e)\)-curves ⋮ Ideal classes of orders in quaternion algebras ⋮ Computing isomorphisms between lattices ⋮ An intriguing hyperelliptic Shimura curve quotient of genus 16 ⋮ On the computation of algebraic modular forms on compact inner forms of 𝐆𝐒𝐩₄ ⋮ Computing with Algebraic Automorphic Forms ⋮ Lattice Methods for Algebraic Modular Forms on Classical Groups ⋮ Evaluating modular forms on Shimura curves ⋮ Examples of abelian surfaces with everywhere good reduction

Uses Software

• Magma
• SageMath

Cites Work

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• The Magma algebra system. I: The user language
• Residually reducible representations and modular forms
• Automorphic forms on GL (2)
• Explicit Computations of Hilbert Modular Forms on ℚ(√5)
• Quaternionic Manin symbols, Brandt matrices, and Hilbert modular forms
• Automorphic Forms on Adele Groups. (AM-83)
• On theta functions of real algebraic number fields
• Determination of elliptic curves with everywhere good reduction over ℚ(√37)
• On the computation of algebraic modular forms on compact inner forms of 𝐆𝐒𝐩₄
• Finding All Elliptic Curves with Good Reduction Outside a Given Set of Primes
• Hecke Eigenvalues for Real Quadratic Fields
• Periods of Hilbert modular surfaces
• Heights of Heegner points on Shimura curves.

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