Israel Journal of Mathematics

, Volume 149, Issue 1, pp 267–299

Ramanujan complexes of typeÃd


DOI: 10.1007/BF02772543

Cite this article as:
Lubotzky, A., Samuels, B. & Vishne, U. Isr. J. Math. (2005) 149: 267. doi:10.1007/BF02772543


We define and construct Ramanujan complexes. These are simplicial complexes which are higher dimensional analogues of Ramanujan graphs (constructed in [LPS]). They are obtained as quotients of the buildings of typeÃd−1 associated with PGLd(F) whereF is a local field of positive characteristic.

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© Hebrew University 2005

Authors and Affiliations

  1. 1.Department of MathematicsThe Hebrew University of JerusalemJerusalemIsrael
  2. 2.Department of MathematicsYale UniversityNew HavenUSA
  3. 3.Department of MathematicsBar-Ilan UniversityRamat GanIsrael