Abstract
dc:description.abstract<p>We construct a spectral triple for the C*-algebra of continuous functions on the space of <em>p</em>-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 <em>D</em> on the tree. Our spectral triple satisfies the properties of a compact spectral metric space and the metric on the space of <em>p</em>-adic integers induced by the spectral triple is equivalent to the usual <em>p</em>-adic metric. Furthermore, we show that the spectrum of the operator <em>D*D </em>is closely related to the roots of a certain <em>q</em>-hypergeometric function and discuss the analytic continuation of the zeta function associated with <em>D*D.</em></p>
Degree
thesis:*- Name thesis:degree_name
- Doctor of Philosophy (PhD)
- Level thesis:degree_level
- Dissertation
- Discipline thesis:degree_discipline
- Mathematics
- Year
- 2015
Author and committee
dc:creator, dc:contributor.*- Author dc:creator
-
- Rathnayake, Sumedha Hemamalee
- Contributors dc:contributor
-
- Slawomir Klimek
- Ronghui Ji
- Carl Cowen
- Marius Dadarlat
Subjects
dc:subject × 1Identifiers
dc:identifier.*- Repository record dc:identifier
- https://docs.lib.purdue.edu/open_access_dissertations/543
- OAI identifier oai:identifier
- oai:docs.lib.purdue.edu:open_access_dissertations-1484