Ramanujan graphs on cosets of PGL2(Fq)

Authors:
Wen-Ching Winnie Li;Yotsanan Meemark
Affiliations:
Department of Mathematics, The Pennsylvania State University, University Park, PA 16802-6401, USA;Department of Mathematics, The Pennsylvania State University, University Park, PA 16802-6401, USA
Venue:
Finite Fields and Their Applications
Year:
2005

Citing 2
Cited 1

Existence and explicit constructions of q+1 regular Ramanujan graphs for every prime power q

Journal of Combinatorial Theory Series B
Character sums over norm groups

Finite Fields and Their Applications

Commutative association schemes

European Journal of Combinatorics

Quantified Score

Hi-index	0.00

Visualization

Abstract

In this paper, we study Cayley graphs on PGL"2(F"q) mod the unipotent subgroup, the split and nonsplit tori, respectively. Using the Kirillov models of the representations of PGL"2(F"q) of degree greater than one, we obtain explicit eigenvalues of these graphs and the corresponding eigenfunctions. Character sum estimates are then used to conclude that two types of the graphs are Ramanujan, while the third is almost Ramanujan. The graphs arising from the nonsplit torus were previously studied by Terras et al. We give a different approach here.