American Institute of Mathematical Sciences

Advanced
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
[1]

François Ledrappier, Seonhee Lim. Volume entropy of hyperbolic buildings. Journal of Modern Dynamics, 2010, 4 (1) : 139-165. doi: 10.3934/jmd.2010.4.139
[2]

Dieter Mayer, Tobias Mühlenbruch, Fredrik Strömberg. The transfer operator for the Hecke triangle groups. Discrete & Continuous Dynamical Systems - A, 2012, 32 (7) : 2453-2484. doi: 10.3934/dcds.2012.32.2453
[3]

Uri Bader, Jan Dymara. Boundary unitary representations—right-angled hyperbolic buildings. Journal of Modern Dynamics, 2016, 10: 413-437. doi: 10.3934/jmd.2016.10.413
[4]

Dieter Mayer, Fredrik Strömberg. Symbolic dynamics for the geodesic flow on Hecke surfaces. Journal of Modern Dynamics, 2008, 2 (4) : 581-627. doi: 10.3934/jmd.2008.2.581
[5]

Frédéric Naud, Anke Pohl, Louis Soares. Fractal Weyl bounds and Hecke triangle groups. Electronic Research Announcements, 2019, 26: 24-35. doi: 10.3934/era.2019.26.003
[6]

Ilwoo Cho, Palle Jorgense. Free probability on $ C^{*}$-algebras induced by hecke algebras over primes. Discrete & Continuous Dynamical Systems - S, 2019, 12 (8) : 2221-2252. doi: 10.3934/dcdss.2019143
[7]

Xingwang Xu, Paul C. Yang. Positivity of Paneitz operators. Discrete & Continuous Dynamical Systems - A, 2001, 7 (2) : 329-342. doi: 10.3934/dcds.2001.7.329
[8]

Dag Lukkassen, Annette Meidell, Peter Wall. Multiscale homogenization of monotone operators. Discrete & Continuous Dynamical Systems - A, 2008, 22 (3) : 711-727. doi: 10.3934/dcds.2008.22.711
[9]

Augusto VisintiN. On the variational representation of monotone operators. Discrete & Continuous Dynamical Systems - S, 2017, 10 (4) : 909-918. doi: 10.3934/dcdss.2017046
[10]

Vincenzo Recupero. Hysteresis operators in metric spaces. Discrete & Continuous Dynamical Systems - S, 2015, 8 (4) : 773-792. doi: 10.3934/dcdss.2015.8.773
[11]

Horst R. Thieme. Remarks on resolvent positive operators and their perturbation. Discrete & Continuous Dynamical Systems - A, 1998, 4 (1) : 73-90. doi: 10.3934/dcds.1998.4.73
[12]

Martin Brokate, Pavel Krejčí. Weak differentiability of scalar hysteresis operators. Discrete & Continuous Dynamical Systems - A, 2015, 35 (6) : 2405-2421. doi: 10.3934/dcds.2015.35.2405
[13]

María José Beltrán, José Bonet, Carmen Fernández. Classical operators on the Hörmander algebras. Discrete & Continuous Dynamical Systems - A, 2015, 35 (2) : 637-652. doi: 10.3934/dcds.2015.35.637
[14]

Bernd Ammann, Robert Lauter and Victor Nistor. Algebras of pseudodifferential operators on complete manifolds. Electronic Research Announcements, 2003, 9: 80-87.

[15]

Eskil Hansen, Alexander Ostermann. Dimension splitting for time dependent operators. Conference Publications, 2009, 2009 (Special) : 322-332. doi: 10.3934/proc.2009.2009.322
[16]

Nils Svanstedt. Multiscale stochastic homogenization of monotone operators. Networks & Heterogeneous Media, 2007, 2 (1) : 181-192. doi: 10.3934/nhm.2007.2.181
[17]

Frédéric Naud. The Ruelle spectrum of generic transfer operators. Discrete & Continuous Dynamical Systems - A, 2012, 32 (7) : 2521-2531. doi: 10.3934/dcds.2012.32.2521
[18]

Dennise García-Beltrán, José A. Vallejo, Yurii Vorobiev. Lie algebroids generated by cohomology operators. Journal of Geometric Mechanics, 2015, 7 (3) : 295-315. doi: 10.3934/jgm.2015.7.295
[19]

Fausto Ferrari. Mean value properties of fractional second order operators. Communications on Pure & Applied Analysis, 2015, 14 (1) : 83-106. doi: 10.3934/cpaa.2015.14.83
[20]

Sarah Constantin, Robert S. Strichartz, Miles Wheeler. Analysis of the Laplacian and spectral operators on the Vicsek set. Communications on Pure & Applied Analysis, 2011, 10 (1) : 1-44. doi: 10.3934/cpaa.2011.10.1

 Impact Factor: 

Tools

Metrics

  • PDF downloads (6)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]

Copyright © 2019 American Institute of Mathematical Sciences