Double-coset zeta functions for groups acting on trees: a local-to-global approach
Geb. 20.30, SR 2.058
Abstract: The double-coset zeta functions, recently introduced by I. Castellano, G. Chinello and T. Weigel, are possible tools for studying asymptotic properties of a locally compact group G. For every fixed compact open subgroup U of G, they are Dirichlet series arising by counting the U-double-cosets with a prescribed Haar measure.
In the seminar talk, we focus on the case where G is a sufficiently transitive group of automorphisms of a locally finite tree. This setting allows us to study the main analytic properties of the series by using a combinatorial and local-to-global approach. We also present a criterion on the group to relate its Euler-Poincaré characteristic and the value of such zeta functions in -1.