Ramanujan graphs on cosets of PGL2 (Fq)

Wen Ching Winnie Li; Yotsanan Meemark

doi:10.1016/j.ffa.2005.05.005

Ramanujan graphs on cosets of PGL₂ (F_q)

Wen Ching Winnie Li
, Yotsanan Meemark

Mathematics

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

In this paper, we study Cayley graphs on PGL₂ (F_q) mod the unipotent subgroup, the split and nonsplit tori, respectively. Using the Kirillov models of the representations of PGL₂ (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.

Original language	English (US)
Pages (from-to)	511-543
Number of pages	33
Journal	Finite Fields and their Applications
Volume	11
Issue number	3
DOIs	https://doi.org/10.1016/j.ffa.2005.05.005
State	Published - Aug 2005

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Algebra and Number Theory
General Engineering
Applied Mathematics

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10.1016/j.ffa.2005.05.005

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title = "Ramanujan graphs on cosets of PGL2 (Fq)",

abstract = "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.",

author = "Li, \{Wen Ching Winnie\} and Yotsanan Meemark",

note = "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.",

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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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DO - 10.1016/j.ffa.2005.05.005

M3 - Article

AN - SCOPUS:23044466129

SN - 1071-5797

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SP - 511

EP - 543

JO - Finite Fields and their Applications

JF - Finite Fields and their Applications

IS - 3

ER -

Ramanujan graphs on cosets of PGL₂ (F_q)

Abstract

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