Modular symbols for Q-rank one groups and Voronoi reduction

Modular symbols for Q-rank one groups and Voronoi reduction Title: Modular symbols for Q-rank one groups and Voronoi reduction
Author: Paul E. Gunnells

Math Subject Class: 11F75

Abstract: 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.

BibTeX

@misc{math.NT/9809058,
    title = {Modular symbols for Q-rank one groups and Voronoi
    reduction},
    author = {Paul E. Gunnells},
    eprint = {math.NT/9809058}}