TY - JOUR
T1 - Ramanujan graphs on cosets of PGL2 (Fq)
AU - Li, Wen Ching Winnie
AU - Meemark, Yotsanan
N1 - Funding Information:
∗ Corresponding author. Fax: +1 814 865 3735. E-mail addresses: [email protected] (W.-C.W. Li), [email protected] (Y. Meemark). 1The research of the first author is supported in part by an NSA grant MDA904-03-1-0069.
PY - 2005/8
Y1 - 2005/8
N2 - In this paper, we study Cayley graphs on PGL2 (Fq) mod the unipotent subgroup, the split and nonsplit tori, respectively. Using the Kirillov models of the representations of PGL2 (Fq) 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.
AB - In this paper, we study Cayley graphs on PGL2 (Fq) mod the unipotent subgroup, the split and nonsplit tori, respectively. Using the Kirillov models of the representations of PGL2 (Fq) 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.
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U2 - 10.1016/j.ffa.2005.05.005
DO - 10.1016/j.ffa.2005.05.005
M3 - Article
AN - SCOPUS:23044466129
SN - 1071-5797
VL - 11
SP - 511
EP - 543
JO - Finite Fields and their Applications
JF - Finite Fields and their Applications
IS - 3
ER -