English

Eigenfunctions on the Finite Poincar\'e Plane

Combinatorics 2008-02-03 v1 Number Theory

Abstract

Let FF be a finite field of odd number of elements. Let F(δ)F(\sqrt{\delta}) be its quadratic extension. F(δ)FF(\sqrt{\delta})-F 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}
}