American Institute of Mathematical Sciences

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2003, 2003(Special): 78-82. doi: 10.3934/proc.2003.2003.78

Ramanujan type graphs and bigraphs

Cristina M. Ballantine 1,

1. 

Department of Mathematics and Computer Science, College of the Holy Cross, Worcester, MA 01609, United States

Received  August 2002 Revised  March 2003 Published  April 2003

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: 20F3.
Citation: Cristina M. Ballantine. Ramanujan type graphs and bigraphs. Conference Publications, 2003, 2003 (Special) : 78-82. doi: 10.3934/proc.2003.2003.78
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