Quaternionic Manin symbols, Brandt matrices, and Hilbert modular forms

DOI10.1090/S0025-5718-06-01914-4zbMath1158.11023OpenAlexW1634195488MaRDI QIDQ3426035

Lassina Dembélé

Publication date: 7 March 2007

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0025-5718-06-01914-4

zbMATH Keywords

automorphic formsHilbert modular formsBrandt matrices

Mathematics Subject Classification ID

Number-theoretic algorithms; complexity (11Y16) Special values of automorphic (L)-series, periods of automorphic forms, cohomology, modular symbols (11F67) Automorphic forms on (mbox{GL}(2)); Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces (11F41)

Related Items (15)

Computing systems of Hecke eigenvalues associated to Hilbert modular forms ⋮ A Simple Trace Formula for Algebraic Modular Forms ⋮ Ideal classes of orders in quaternion algebras ⋮ SERRE WEIGHTS AND WILD RAMIFICATION IN TWO-DIMENSIONAL GALOIS REPRESENTATIONS ⋮ On computing quaternion quotient graphs for function fields ⋮ Computing Hilbert Modular Forms over Fields with Nontrivial Class Group ⋮ Hecke Operators and Hilbert Modular Forms ⋮ On the computation of algebraic modular forms on compact inner forms of 𝐆𝐒𝐩₄ ⋮ Syntomic regulators of Asai-Flach classes ⋮ Explicit Calculations of Automorphic Forms for Definite Unitary Groups ⋮ Computing with Algebraic Automorphic Forms ⋮ Lattice Methods for Algebraic Modular Forms on Classical Groups ⋮ Recipes to Fermat-type equations of the form \(x^r + y^r =Cz^p\) ⋮ Evaluating modular forms on Shimura curves ⋮ Nonvanishing of twists of -functions attached to Hilbert modular forms

Uses Software

• Magma

Cites Work

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• Unramified Hilbert modular forms, with examples relating to elliptic curves
• On Galois representations associated to Hilbert modular forms
• An algorithm for computing modular forms on \(\Gamma_0(N)\)
• The special values of the zeta functions associated with Hilbert modular forms
• Algebraic modular forms
• Automorphic forms on GL (2)
• Explicit Computations of Hilbert Modular Forms on ℚ(√5)
• Automorphic Forms on Adele Groups. (AM-83)
• ARITHMETIC ON A QUINTIC THREEFOLD

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