Representation zeta functions of self-similar branched groups
Laurent Bartholdi
Universität Göttingen, Germany
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Abstract
We compute the numbers of irreducible linear representations of self-similar branched groups, by expressing these numbers as the coëfficients of a Dirichlet series .
We show that this Dirichlet series has a positive abscissa of convergence and satisfies a functional equation thanks to which it can be analytically continued (through root singularities) to the right half-plane.
We compute the abscissa of convergence and the functional equation for some prominent examples of branched groups, such as the Grigorchuk and Gupta–Sidki groups.
Cite this article
Laurent Bartholdi, Representation zeta functions of self-similar branched groups. Groups Geom. Dyn. 11 (2017), no. 1, pp. 29–56
DOI 10.4171/GGD/386