Modular Symbols for Q-rank One Groups and Voronoǐ Reduction
نویسنده
چکیده
Let G be a reductive algebraic group of Q-rank one associated to a self-adjoint homogeneous cone defined over Q, and let Γ ⊂ G be a torsion-free arithmetic subgroup. Let d be the cohomological dimension of Γ. We present an algorithm to compute the action of the Hecke operators on H(Γ;Z). This generalizes the classical modular symbol algorithm, when Γ ⊂ SL2(Z), to a setting including Bianchi groups and Hilbert modular groups. In addition, we generalize some results of Voronǒı for real positive-definite quadratic forms to self-adjoint homogeneous cones of arbitrary Q-rank.
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