Ramanujan type graphs and bigraphs
Cristina M. Ballantine
We show that quotients of the Bruhat-Tits building of S$L_3(mathbb(Q)_p)$ form an infinite family of graphs which are Ramanujan type. We investigate the Bruhat-Tits tree associated with U$_3(mathbb(Q)_p)$ and show how its relation to the building of S$L_3(mathbb(Q)_p)$should lead to an estimation of its spectrum.
keywords: Hecke operators Buildings.

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