Computing topological zeta functions of groups, algebras, and modules, I

2014/05/22 by Tobias Rossmann, Rossmann, Tobias · 1 citation
Mathematics · #11M41 #14M25 #20F69 #Algebraic Geometry (math.AG) #FOS: Mathematics #Group Theory (math.GR) #Number Theory (math.NT) #math.AG #math.GR #math.NT #msc:11M41 #msc:14M25 #msc:20F69

paper · pdf · doi:10.48550/arxiv.1405.5711

42 pages

arxiv created 2014/05/22 · arxiv updated 2014/05/23

Abstract

We develop techniques for computing zeta functions associated with nilpotent groups, not necessarily associative algebras, and modules, as well as Igusa-type zeta functions. At the heart of our method lies an explicit convex-geometric formula for a class of p-adic integrals under non-degeneracy conditions with respect to associated Newton polytopes. Our techniques prove to be especially useful for the computation of topological zeta functions associated with algebras, resulting in the first systematic investigation of their properties.

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• Computing topological zeta functions of groups, algebras, and modules, II

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