Representation zeta functions of self-similar branched groups
2017 | journal article; research paper. A publication with affiliation to the University of Göttingen.
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- Authors
- Bartholdi, Laurent
- Abstract
- We compute the numbers of irreducible linear representations of self-similar branched groups, by expressing these numbers as the coefficients r(n) of a Dirichlet series Sigma r(n)n(-s). 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.
- Issue Date
- 2017
- Journal
- Groups, Geometry, and Dynamics
- Organization
- Mathematisches Institut
- ISSN
- 1661-7207
- ISSN
- 1661-7215; 1661-7207
- Language
- English