Eigenfunctions on the Finite Poincar\'e Plane
Combinatorics
2008-02-03 v1 Number Theory
Abstract
Let be a finite field of odd number of elements. Let be its quadratic extension. is the so-called finite Poincare plane. This paper relates the bases of eigenfunctions constructed by Evans and by Kuang. The finite Poincare plane can be viewed as a Ramanujan graph. This paper also provides evidence for Terras' conjecture regarding the asymptotic distribution of the eigenvalus of the adjacency matrices.
Cite
@article{arxiv.math/9411217,
title = {Eigenfunctions on the Finite Poincar\'e Plane},
author = {Jinghua Kuang},
journal= {arXiv preprint arXiv:math/9411217},
year = {2008}
}