Descript 
64 p 
Note 
Source: Dissertation Abstracts International, Volume: 7109, Section: B, page: 5508 

Adviser: WenChing Winnie Li 

Thesis (Ph.D.)The Pennsylvania State University, 2010 

In the first part of this thesis, we study the zeta functions of complexes arising from PGL3 over a nonarchimedean local field. In this case, the complexes have dimension two. We define several zeta functions on the complexes; each of them counts the number of tailless geodesic cycles of certain type and dimension. These zeta functions are rational functions and have closed form expressions in terms of parahoric Hecke operators. The main result of the thesis is showing that the alternating product of these zeta functions satisfies a zeta identity involving the Euler characteristic of the complex and the characteristic polynomial of the recurrence relations of the Hecke algebra. Further, we obtain an equivalent criterion for Ramanujan complex in terms of the distributions of poles of the zeta functions 

The second part of the thesis is an application of group theory and graph theory in chemistry. We classify the fullerenes with Cayley graph structure and show that excepted for C60, the remaining fullerene Cayley graph are toroidal provided that they are orientable. We give an explicit expression of the spectra of these graphs using the characters of some abelian groups. In the end, we construct a family of fullerene Cayley graphs with a prescribed HOMOLUMO gap and study how to realize them in threedimensional space 

School code: 0176 
Host Item 
Dissertation Abstracts International 7109B

Subject 
Mathematics


0405

Alt Author 
The Pennsylvania State University

