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Ramanujan type graphs and bigraphs

Pages: 78 - 82, Issue Special, July 2003

 Abstract        Full Text (205.2K)              

Cristina M. Ballantine - Department of Mathematics and Computer Science, College of the Holy Cross, Worcester, MA 01609, United States (email)

Abstract: 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.
Mathematics Subject Classification:  Primary: 11F25; Secondary: 20F32.

Received: August 2002;      Revised: March 2003;      Published: April 2003.