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On eigenvalues of p-adic curvature

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Abstract

We study the eigenvalues of the p-adic curvature transformationson buildings. In particular, we determine the maximal eigenvalues ofthese transformations.

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References

  1. Ballantine C.: Ramanujan type buildings. Can. J. Math. 52, 1121–1148 (2000)

    MATH  MathSciNet  Google Scholar 

  2. Ballantine C.: A hypergraph with commuting partiallaplacians. Can. Math. Bull. 44, 385–397 (2001)

    MATH  MathSciNet  Google Scholar 

  3. Berkovich V.: Spectral theory and analytic geometry over non-Archimedean fields. Mathematical Surveys and Monographs, 33. Am. Math. Soc., Providence, RI (1990)

    Google Scholar 

  4. Bıyıkoǧlu T., Leydold J., Stadler P.: Laplacian eigenvectors of graphs, LNM 1915. Springer, Heidelberg (2007)

    Google Scholar 

  5. Borel, A.: Cohomologie decertains groupes discretes et laplacien p-adique. (d’après H.Garland), Séminaire Bourbaki, exp. no. 437 (1973)

  6. Brown K.: Buildings. Springer, Heidelberg (1989)

    MATH  Google Scholar 

  7. Bruhat F., Tits J.: Groupes réductifs sur un corps local I. Publ. Math. IHÉS 41, 5–251 (1972)

    MATH  MathSciNet  Google Scholar 

  8. Casselman W.: On a p-adic vanishing theorem of Garland. Bull. Am. Math. Soc. 80, 1001–1004 (1974)

    Article  MATH  MathSciNet  Google Scholar 

  9. Chung F.R.K.: Spectral graph theory. CBMS Regional Conference Series in Mathematics, 92. Am. Math. Soc., Providence, RI (1997)

    Google Scholar 

  10. Dymara J., Januszkiewicz T.: Cohomology of buildings and their automorphism groups. Invent. Math. 150, 579–627 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  11. Feit W., Higman G.: The non-existence of certain generalized polygons. J. Algebra 1, 114–131 (1964)

    Article  MATH  MathSciNet  Google Scholar 

  12. Garland H.: p-adic curvature and the cohomology of discrete groups. Ann. Math. 97, 375–423 (1973)

    Article  MathSciNet  Google Scholar 

  13. Li W.-C.W.: Ramanujan hypergraphs. Geom. Funct. Anal. 14, 380–399 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  14. Lubotzky A., Samuels B., Vishne U.: Ramanujan complexes of type à d . Isr. J. Math. 149, 267–299 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  15. Żuk A.: Property (T) and Kazhdan constants for discrete groups. Geom. Funct. Anal. 13, 643–670 (2003)

    Article  MATH  MathSciNet  Google Scholar 

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  1. Department of Mathematics, Pennsylvania State University, University Park, PA, 16802, USA

    Mihran Papikian

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  1. Mihran Papikian
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Correspondence to Mihran Papikian.

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Papikian, M. On eigenvalues of p-adic curvature. manuscripta math. 127, 397–410 (2008). https://doi.org/10.1007/s00229-008-0216-5

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  • DOI: https://doi.org/10.1007/s00229-008-0216-5

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