Date of Award
Spring 2015
Degree Type
Dissertation
Degree Name
Doctor of Philosophy (PhD)
Department
Mathematics
First Advisor
Slawomir Klimek
Committee Chair
Slawomir Klimek
Committee Member 1
Ronghui Ji
Committee Member 2
Carl Cowen
Committee Member 3
Marius Dadarlat
Abstract
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.
Recommended Citation
Rathnayake, Sumedha Hemamalee, "A p-adic spectral triple" (2015). Open Access Dissertations. 543.
https://docs.lib.purdue.edu/open_access_dissertations/543