A graph theoretical analogue of Brauer-Siegel theory for zeta functions of number Â…elds is developed using the theory of Artin L-functions for Galois coverings of graphs from parts I and II. In theâ€¦ (More)

Some of the research surveyed here was supported by the Mathematical Sciences Research Institute in Berkeley, CA. Research at MSRI is supported in part by NSF grant DMS-9022140. We survey what isâ€¦ (More)

We discuss zeta functions of finite irregular undirected connected graphs (which may be weighted) and apply them to obtain, for example an analog of the prime number theorem for cycles in graphs. Weâ€¦ (More)

We consider complex-valued modular forms on nite upper half planes Hq and obtain Fourier expansions of Eisenstein series invariant under the groups 0 D SL.2;Fp/ and GL.2;Fp/: The expansions areâ€¦ (More)

We present examples of hypergraphs constructed from homogeneous spaces of finite general linear groups. These hypergraphs are constructed using an invariant analogue of a hypervolume and theirâ€¦ (More)

I will compare spectra from physics, geometry and number theory with spectra arising from Cayley graphs of matrix groups. The methods come from group representations and the theory of Artinâ€¦ (More)

We nd a condition for weights on the edges of a graph which insures that the Ihara zeta function has a 3-term determinant formula. Then we investigate the locations of poles of abelian graphâ€¦ (More)