ZETA FUNCTIONS OF DISCRETE GROUPS ACTING ON TREES
ZETA FUNCTIONS OF DISCRETE GROUPS ACTING ON TREES
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作用于树木的离散群的 ZETA 函数
DOI：
10.1006/jabr.2000.8600
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发表时间：
1999
影响因子：
0.9
通讯作者：
Shahriar Mokhtari
中科院分区：
文献类型：
--
作者：
Bryan Clair;Shahriar Mokhtari
摘要本文推广了一致树格上的zeta函数的Bass工作。利用冯·诺伊曼代数理论，建立了定义有界度树离散自同构群的zeta函数的机制。主要定理将ζ函数与定义在树的边或顶点上的算子的行列式联系起来。定义了与具有适当希尔伯特表示的非均匀树格相关联的zeta函数。对于具有紧或有限协卷群作用的无限图，定义了Zeta函数。
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.