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Topological representation zeta functions of unipotent groups
Inspired by work surrounding Igusa's local zeta function, we introduce
topological representation zeta functions of unipotent algebraic groups over
number fields. These group-theoretic invariants capture common features of
established -adic representation zeta functions associated with pro-
groups derived from unipotent groups. We investigate fundamental properties of
the topological zeta functions considered here. We also develop a method for
computing them under non-degeneracy assumptions. As an application, among other
things, we obtain a complete classification of topological representation zeta
functions of unipotent algebraic groups of dimension at most six.Comment: 27 page
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