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Zeta Functions Of Discrete Groups Acting On Trees

Bryan Clair·Shahriar Mokhtari-Sharghi
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Abstract

This paper generalizes Bass' work on zeta functions for uniform tree lattices. Using the theory of von Neumann algebras, machinery is developed to define the zeta function of a discrete group of automorphisms of a bounded degree tree. The main theorems relate the zeta function to determinants of operators defined on edges or vertices of the tree. A zeta function associated to a non-uniform tree lattice with appropriate Hilbert representation is defined. Zeta functions are defined for infinite graphs with a cocompact or finite covolume group action.

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BibTeXRIS

Bryan Clair, Shahriar Mokhtari-Sharghi. 1999-08-14. Zeta Functions Of Discrete Groups Acting On Trees. https://arxiv.org/abs/math/9908068

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