✦ LIBER ✦
Modular Symbols for Q-Rank One Groups and Voronı Reduction
✍ Scribed by Paul E Gunnells
- Publisher
- Elsevier Science
- Year
- 1999
- Tongue
- English
- Weight
- 220 KB
- Volume
- 75
- Category
- Article
- ISSN
- 0022-314X
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✦ Synopsis
Let G be a reductive algebraic group of Q-rank one associated to a self-adjoint homogeneous cone defined over Q, and let 1/G be a torsion-free arithmetic subgroup. Let d be the cohomological dimension of 1. We present an algorithm to compute the action of the Hecke operators on H d (1; Z). This generalizes the classical modular symbol algorithm, when 1/SL 2 (Z), to a setting including Bianchi groups and Hilbert modular groups. In addition, we generalize some results of Vorono@ for real positive-definite quadratic forms to self-adjoint homogeneous cones of arbitrary Q-rank.