The Ramanujan Property for Regular Cubical Complexes

@inproceedings{Jordan2000TheRP,
  title={The Ramanujan Property for Regular Cubical Complexes},
  author={Bruce W M Jordan and RON LIVN{\'E}},
  year={2000}
}
We consider cubical complexes which are uniformized by an ordered product of regular trees. For these we define the notion of being Ramanujan, generalizing the one-dimensional definition introduced by Lubotzky, Phillips, and Sarnak [15]. As in [12], we also allow local systems. We discuss the significance of this property, and then we construct explicit arithmetic examples using quaternion algebras over totally real fields. Here we reduce the Ramanujan property to special cases of the Ramanujan… CONTINUE READING

From This Paper

Topics from this paper.

References

Publications referenced by this paper.
Showing 1-10 of 21 references

Ramanujan local systems on graphs

B. W. Jordan, R. Livné
Topology 36 • 1997
View 8 Excerpts
Highly Influenced

Ramanujan graphs

View 6 Excerpts
Highly Influenced

Actions of Cartan subgroups

S. Mozes
Israel J. of Math. 90 • 1995
View 2 Excerpts

Integral Hodge theory and congruences between modular forms

B. W. Jordan, R. Livné
Duke Math. J. 80 • 1995

Spherical functions and Ramanujan conjecture . In : Algebraic Groups and Discontinuous Subgroups

I. Satake
Israel J . of Math . • 1995

Discrete Groups

A. Lubotzky
Expanding Graphs and Invariant Measures, Birkhäuser Verlag, Basel- Boston-Berlin • 1994
View 1 Excerpt

Motives for Hilbert modular forms

D. Blasius, J. D. Rogawski
Invent. math. 114 • 1993
View 1 Excerpt

Cubic Ramanujan graphs

Combinatorica • 1992
View 1 Excerpt

Expanders and diffusers

M. W. Buck
SIAM J. Alg. Disc. Math. 7 • 1986
View 1 Excerpt

Similar Papers

Loading similar papers…