Modular symbols for Q-rank one groups and Voronoi reduction

1998/09/10 by Paul E. Gunnells, Gunnells, Paul E. · 1 citation
Mathematics · #11F75 #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11F75

paper · pdf · doi:10.48550/arxiv.math/9809058

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

arxiv created 1998/09/10 · arxiv updated 2009/11/30

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.

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• A full-rank subgroup of Bloch Groups of CM Fields

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