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On non-uniform Ramanujan complexes


Author: Beth Samuels
Journal: Proc. Amer. Math. Soc. 137 (2009), 2869-2877
MSC (2000): Primary 11F70
DOI: https://doi.org/10.1090/S0002-9939-09-09880-3
Published electronically: April 17, 2009
MathSciNet review: 2506444
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  • [A] J. Arthur, Eisenstein series and the trace formula, in Automorphic Forms, Representa- tions, and $ L$-functions, Proc. Sympos. Pure Math. XXXIII, eds. A. Borel and W. Casselman, Amer. Math. Soc., pp. 253-274, 1979. MR 546601 (81b:10020)
  • [J] H. Jacquet, On the residual spectrum of $ {\rm GL}(n)$, in Lie group representations, II (College Park, Md., 1982/1983), eds. R. Herb, S. Kudla, R. Lipsman and J. Rosenberg, Lecture Notes in Math. 1041, Springer, pp. 185-208, 1984. MR 748508 (85k:22045)
  • [JS] H. Jacquet and J. Shalika, Sur le spectre résiduel du groupe linéaire [On the residual spectrum of the linear group], C. R. Acad. Sci. Paris Sér. I Math. 293 (11) (1981), 541-543. MR 647676 (83a:10050)
  • [La] L. Lafforgue, Chtoucas de Drinfeld et correspondance de Langlands (French), Invent. Math. 147 (1) (2002), 1-241. MR 1875184 (2002m:11039)
  • [Li] W.-C. W. Li, Ramanujan hypergraphs, Geometric and Functional Analysis 14 (2004), 380-399. MR 2060199 (2005i:11172)
  • [Lu] A. Lubotzky, Discrete Groups, Expanding Graphs and Invariant Measures, Progress in Math. 125, Birkhäuser, 1994. MR 1308046 (96g:22018)
  • [LPS] A. Lubotzky, R. Philips and P. Sarnak, Ramanujan graphs, Combinatorica 8 (1988), 261-277. MR 963118 (89m:05099)
  • [LSV1] A. Lubotzky, B. Samuels and U. Vishne, Ramanujan complexes of type $ \tilde{A}_d$, Israel J. Math. 149 (2005), 267-299. MR 2191217 (2006i:11134)
  • [LSV2] A. Lubotzky, B. Samuels and U. Vishne, Explicit constructions of Ramanujan complexes of type $ \tilde{A}_d$, European J. Combinatorics 26 (6) (2005), 965-993. MR 2143204 (2006g:20043)
  • [MW] C. Mœglin and J.-L. Waldspurger, Le spectre résidual de $ {GL}(n)$, Ann. Scient. École Norm. Sup., $ 4^{e}$ série 22 (1989), 605-674. MR 1026752 (91b:22028)
  • [M1] M. Morgenstern, Existence and explicit constructions of $ q+1$ regular Ramanujan graphs for every prime power $ q$, J. Combin. Theory Ser. B 62 (1) (1994), 44-62. MR 1290630 (95h:05089)
  • [M2] M. Morgenstern, Ramanujan diagrams, SIAM J. Discrete Math. 7 (4) (1994), 560-570. MR 1299084 (96g:05076)
  • [M3] M. Morgenstern, Natural bounded concentrators, Combinatorica 15 (1) (1995), 111-122. MR 1325275 (96f:05106)
  • [OW] M.S. Osborne and G. Warner, The Theory of Eisenstein Systems, Academic Press, 1981. MR 643242 (83j:10034)
  • [S] B. Samuels, ``Ramanujan complexes, non-uniform quotients and isospectrality'', Ph.D. thesis, Yale University, 2005.
  • [Sa] A. Sarveniazi, Explicit construction of a Ramanujan $ (n\sb 1,n\sb 2,\dots,n\sb {d-1})$-regular hypergraph, Duke Math. J. 139 (2007), no. 1, 141-171. MR 2322678 (2008k:11055)

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Additional Information

Beth Samuels
Affiliation: (A. Lubotzky) Institute of Mathematics, Hebrew University, Givat-Ram, Jerusalem 91904, Israel; (U. Vishne) Department of Mathematics, Bar-Ilan University, Ramat-Gan 52900, Israel
Email: alexlub@math.huji.ac.il, vishne@math.biu.ac.il

DOI: https://doi.org/10.1090/S0002-9939-09-09880-3
Received by editor(s): April 7, 2008
Received by editor(s) in revised form: December 1, 2008
Published electronically: April 17, 2009
Additional Notes: Posthumous, based on Chapter 3 of the author’s Ph.D. thesis. Prepared for publication by Alex Lubotzky and Uzi Vishne
Communicated by: Wen-Ching Winnie Li
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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