On non-uniform Ramanujan complexes
HTML articles powered by AMS MathViewer
- by Beth Samuels PDF
- Proc. Amer. Math. Soc. 137 (2009), 2869-2877 Request permission
References
- James Arthur, Eisenstein series and the trace formula, Automorphic forms, representations and $L$-functions (Proc. Sympos. Pure Math., Oregon State Univ., Corvallis, Ore., 1977) Proc. Sympos. Pure Math., XXXIII, Amer. Math. Soc., Providence, R.I., 1979, pp. 253â274. MR 546601
- HervĂ© Jacquet, On the residual spectrum of $\textrm {GL}(n)$, Lie group representations, II (College Park, Md., 1982/1983) Lecture Notes in Math., vol. 1041, Springer, Berlin, 1984, pp. 185â208. MR 748508, DOI 10.1007/BFb0073148
- HervĂ© Jacquet and Joseph Shalika, Sur le spectre rĂ©siduel du groupe linĂ©aire, C. R. Acad. Sci. Paris SĂ©r. I Math. 293 (1981), no. 11, 541â543 (French, with English summary). MR 647676
- Laurent Lafforgue, Chtoucas de Drinfeld et correspondance de Langlands, Invent. Math. 147 (2002), no. 1, 1â241 (French, with English and French summaries). MR 1875184, DOI 10.1007/s002220100174
- W.-C. W. Li, Ramanujan hypergraphs, Geom. Funct. Anal. 14 (2004), no. 2, 380â399. MR 2060199, DOI 10.1007/s00039-004-0461-z
- Alexander Lubotzky, Discrete groups, expanding graphs and invariant measures, Progress in Mathematics, vol. 125, BirkhÀuser Verlag, Basel, 1994. With an appendix by Jonathan D. Rogawski. MR 1308046, DOI 10.1007/978-3-0346-0332-4
- A. Lubotzky, R. Phillips, and P. Sarnak, Ramanujan graphs, Combinatorica 8 (1988), no. 3, 261â277. MR 963118, DOI 10.1007/BF02126799
- Alexander Lubotzky, Beth Samuels, and Uzi Vishne, Ramanujan complexes of type $\~A_d$, Israel J. Math. 149 (2005), 267â299. Probability in mathematics. MR 2191217, DOI 10.1007/BF02772543
- Alexander Lubotzky, Beth Samuels, and Uzi Vishne, Explicit constructions of Ramanujan complexes of type $\~A_d$, European J. Combin. 26 (2005), no. 6, 965â993. MR 2143204, DOI 10.1016/j.ejc.2004.06.007
- C. MĆglin and J.-L. Waldspurger, Le spectre rĂ©siduel de $\textrm {GL}(n)$, Ann. Sci. Ăcole Norm. Sup. (4) 22 (1989), no. 4, 605â674 (French). MR 1026752
- Moshe Morgenstern, Existence and explicit constructions of $q+1$ regular Ramanujan graphs for every prime power $q$, J. Combin. Theory Ser. B 62 (1994), no. 1, 44â62. MR 1290630, DOI 10.1006/jctb.1994.1054
- Moshe Morgenstern, Ramanujan diagrams, SIAM J. Discrete Math. 7 (1994), no. 4, 560â570. MR 1299084, DOI 10.1137/S0895480192235325
- Moshe Morgenstern, Natural bounded concentrators, Combinatorica 15 (1995), no. 1, 111â122. MR 1325275, DOI 10.1007/BF01294463
- M. Scott Osborne and Garth Warner, The theory of Eisenstein systems, Pure and Applied Mathematics, vol. 99, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1981. MR 643242 [S]Thesis B. Samuels, âRamanujan complexes, non-uniform quotients and isospectralityâ, Ph.D. thesis, Yale University, 2005.
- Alireza Sarveniazi, Explicit construction of a Ramanujan $(n_1,n_2,\dots ,n_{d-1})$-regular hypergraph, Duke Math. J. 139 (2007), no. 1, 141â171. MR 2322678, DOI 10.1215/S0012-7094-07-13913-9
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
- 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 authorâs Ph.D. thesis. Prepared for publication by Alex Lubotzky and Uzi Vishne
- Communicated by: Wen-Ching Winnie Li
- © Copyright 2009
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 137 (2009), 2869-2877
- MSC (2000): Primary 11F70
- DOI: https://doi.org/10.1090/S0002-9939-09-09880-3
- MathSciNet review: 2506444