2 citations · 3 across the 5 of their papers we have counts for
6 papers
The Ihara zeta function of the infinite grid
Bryan Clair
The infinite grid is the Cayley graph of with the usual generators. In this paper, the Ihara zeta function for the infinite grid is computed using el…
Zeta functions of graphs with actions
Bryan Clair
Suppose is a regular covering of a graph with covering transformation group . This paper gives an explicit formula for the zeta function of and com…
Growth of Betti Numbers
Bryan Clair, Kevin Whyte
Suppose X is any finite complex with vanishing L^2 Betti number. We prove upper bounds on the Betti numbers for regular coverings of X, sublinear in the order of covering. The boun…
Convergence of zeta functions of graphs
Bryan Clair, Shahriar Mokhtari-Sharghi
The -zeta function of an infinite graph Y (defined previously in a ball around zero) has an analytic extension. For a tower of finite graphs covered by Y, the normalized zeta…
Zeta Functions Of Discrete Groups Acting On Trees
Bryan Clair, Shahriar Mokhtari-Sharghi
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 dis…
Residual Amenability and the Approximation of L^2-invariants
Bryan Clair
We generalize Luck's Theorem to show that the L^2-Betti numbers of a residually amenable covering space are the limit of the L^2-Betti numbers of a sequence of amenable covering sp…