Date of Award

Spring 2015

Degree Type


Degree Name

Doctor of Philosophy (PhD)



First Advisor

Slawomir Klimek

Committee Chair

Slawomir Klimek

Committee Member 1

Ronghui Ji

Committee Member 2

Carl Cowen

Committee Member 3

Marius Dadarlat


We construct a spectral triple for the C*-algebra of continuous functions on the space of p-adic integers. On the technical level we utilize a weighted rooted tree obtained from a coarse grained approximation of the space combined with the forward derivative D on the tree. Our spectral triple satisfies the properties of a compact spectral metric space and the metric on the space of p-adic integers induced by the spectral triple is equivalent to the usual p-adic metric. Furthermore, we show that the spectrum of the operator D*D is closely related to the roots of a certain q-hypergeometric function and discuss the analytic continuation of the zeta function associated with D*D.

Included in

Mathematics Commons