Modular symbols for Q-rank one groups and Voronoi reduction

Details Modular symbols for Q-rank one groups and Voronoi reduction Modular symbols for Q-rank one groups and Voronoi reduction

1998-09-10

arxiv.org/abs/math/9809058v1

Mathematics

Number Theory

19 pages, 5 figures, AMS-LaTeX, uses psfrag.sty, to appear in Journal of Number Theory

Scientific paper

We present an algorithm to compute the action of the Hecke operators on the top dimensional integral cohomology of certain torsion-free arithmetic subgroups of algebraic groups of Q-rank one. This generalizes the modular symbol algorithm to a setting including Bianchi groups and Hilbert modular groups. In addition, we generalize some results of Voronoi for real positive-definite quadratic forms to self-adjoint homogeneous cones of arbitrary Q-rank.

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