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Zeta Functions of Discrete Groups Acting on Trees

✍ Scribed by Bryan Clair; Shahriar Mokhtari-Sharghi

Publisher: Elsevier Science
Year: 2001
Tongue: English
Weight: 198 KB
Volume: 237
Category: Article
ISSN: 0021-8693
DOI: 10.1006/jabr.2000.8600

No coin nor oath required. For personal study only.

✦ Synopsis

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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