Ramanujan graphs on cosets of PGL2 (Fq)

Wen-ching Winnie Li, Yotsanan Meemark

Research output: Contribution to journalArticle

5 Citations (Scopus)

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.

Original languageEnglish (US)
Pages (from-to)511-543
Number of pages33
JournalFinite Fields and their Applications
Volume11
Issue number3
DOIs
StatePublished - Aug 1 2005

Fingerprint

Ramanujan Graphs
Coset
Eigenvalues and eigenfunctions
Ramanujan
Torus
Graph in graph theory
Character Sums
Cayley Graph
Eigenfunctions
Subgroup
Eigenvalue
Estimate
Model

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Algebra and Number Theory
  • Engineering(all)
  • Applied Mathematics

Cite this

Li, Wen-ching Winnie ; Meemark, Yotsanan. / Ramanujan graphs on cosets of PGL2 (Fq). In: Finite Fields and their Applications. 2005 ; Vol. 11, No. 3. pp. 511-543.
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Ramanujan graphs on cosets of PGL2 (Fq). / Li, Wen-ching Winnie; Meemark, Yotsanan.

In: Finite Fields and their Applications, Vol. 11, No. 3, 01.08.2005, p. 511-543.

Research output: Contribution to journalArticle

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