%0 Journal Article
%T Ramanujan bigraphs associated with SU(3) over a p-adic field
%A Cristina Ballantine
%A Dan Ciubotaru
%J Mathematics
%D 2010
%I arXiv
%X We use the representation theory of the quasisplit form G of SU(3) over a p-adic field to investigate whether certain quotients of the Bruhat--Tits tree associated to this form are Ramanujan bigraphs. We show that a quotient of the tree associated with G (which is a biregular bigraph) is Ramanujan if and only if G satisfies a Ramanujan type conjecture. This result is analogous to the seminal case of PGL(2) considered by Lubotzky-Phillips-Sarnak. As a consequence, the classification by Rogawski of the automorphic spectrum of U(3) implies the existence of certain infinite families of Ramanujan bigraphs.
%U http://arxiv.org/abs/1005.3504v1