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On liftings and cusp cohomology of arithmetic groups

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References

  1. Borel, A.: Stable real cohomology of arithmetic groups II. In: Hano, J., et al. (eds.) Manifolds and Lie groups. Progress in Maths., vol. 14, pp. 21–55. Boston-Basel-Stuttgart: Birkhäuser 1981

    Google Scholar 

  2. Borel, A.:Automorphic L-functions. In: Proc. Symp. Pure Maths., vol. 33, part 2, pp. 27–62. Providence: AMS 1979

    Google Scholar 

  3. Borel, A.: Cohomology of arithmetic groups. In: Proc. Int. Congress Math. Vancouver, vol. I, pp. 435–442, Vancouver 1974

  4. Borel, A., Wallach, N.: Continuous cohomology, discrete subgroups and representations of reductive groups. Ann. Math. Stud.94, Princeton: University Press 1980

    Google Scholar 

  5. Brylinski, J.-L., Labesse, J.-P.: Cohomologie d'intersection et fonctionsL de certaines variétés de Shimura. Ann. Sci. Éc. Norm. Super. (4),17, 361–412 (1984)

    Google Scholar 

  6. Clozel, L.: On limit multiplicities of discrete series representations in spaces of automorphic forms. Preprint 1985

  7. Clozel, L., Delorme, P.: Pseudo-coefficients et cohomologie des groupes de Lie réductifs reels. C.R. Acad. Sci. Paris300, 385–387 (1985)

    Google Scholar 

  8. Duflo, M., Labesse, J.-P.: Sur la formule des traces de Selberg. Ann. Sci. Éc. Norm. Super. (4)4 193–284 (1971)

    Google Scholar 

  9. Ehrenpreis, L., Mautner, F.F.: Some properties of the Fouriertransforms on semisimple Lie groups. II. Trans. Am. Math. Soc.84, 1–55 (1957)

    Google Scholar 

  10. Elstrodt, J., Grunewald, F., Mennicke, J.: Discontinuous groups on hyperbolic 3-space and number theoretic applications. Preprint 1985

  11. Enright, T.J.: Relative Lie algebra cohomology and unitary representations of complex Lie groups. Duke Math. J.46, 513–525 (1979)

    Google Scholar 

  12. Flath, D.: A comparison of the automorphic forms ofGL(3) and its twisted forms. Pac. J. Math.97, 373–402 (1981)

    Google Scholar 

  13. Gelbart, S.: Automorphic forms on adele groups. Ann. Math. Stud.83, Princeton: University Press 1975

    Google Scholar 

  14. Gelbart, S., Jacquet, H.: A relation between automorphic representations ofGL(2) andGL(3). Ann. Sci. Éc. Norm. Super. (4)11, 471–542 (1978)

    Google Scholar 

  15. Gelbart, S., Knapp, A.: Irreducible constituents of principal series ofSL n(k) Duke Math. J.48, 313–326 (1981)

    Google Scholar 

  16. Gelbart, S., Knapp, A.:L-indistinguishability andR groups for the special linear group. Adv. Math.43, 101–121 (1982)

    Google Scholar 

  17. Grunewald, F., Schwermer, J.: A non-vanishing theorem for the cuspidal cohomology ofSL 2 over imaginary quadratic integers. Math. Ann.258, 183–200 (1981)

    Google Scholar 

  18. Harder, G.: On the cohomology of\(SL_2 (\mathcal{O})\). In: Gelfand, I.M. (ed.) Lie groups and their representations, pp. 139–150. London: Hilger 1975

    Google Scholar 

  19. Jacquet, H., Langlands, R.P.: Automorphic forms onGL(2) Lect. Notes in Maths., vol114. Berlin-Heidelberg-New York: Springer 1970

    Google Scholar 

  20. Jacquet, H., Piatetski-Shapiro, I.I., Shalika, J.: Relevement cubique non normal. C.R. Acad. Sci. Paris292, 567–571 (1981)

    Google Scholar 

  21. Kneser, M.: Strong approximation. In: Proc. Symp. Pure Maths., vol. 9, pp. 187–196. Providence: AMS 1966

    Google Scholar 

  22. Labesse, J.-P.: Formule des traces et fonction ζ Г de Ihara., In: Variétés de Shimura et fonctionsL. Publ. Math. de l'Univ. Paris VII, vol. 6, pp. 165–178. Paris 1979

  23. Labesse, J.-P., Langlands, R.P.:L-indistinguishability forSL(2) Can. J. Math.31, 726–785 (1979)

    Google Scholar 

  24. Langlands, R.P.: Modular forms andl-adic representations. In: Modular functions of one variable II, Lect. Notes in Maths., vol. 349 pp. 361–500. Berlin-Heidelberg-New York: Springer 1973

    Google Scholar 

  25. Langlands, R.P.: On the classification of irreducible representations of real algebraic groups. Mimeographed notes. IAS Princeton 1973

  26. Langlands, R.P.: On the notion of an automorphic representation. Proc. Symp. Pure Maths., vol. 33, part 1, pp. 203–207 Providence: AMS, 1979

    Google Scholar 

  27. Langlands, R.P.: Automorphic representations, Shimura varieties and motives. Ein Märchen. In: Proc. Symp. Pure Maths., vol. 33, part 2, pp. 205–246. Providence: AMS 1979

    Google Scholar 

  28. Langlands, R.P.: Base change forGL(2). Annals of Math. Studies96. Princeton: University Press 1980

    Google Scholar 

  29. Lee, R., Schwermer, J.: The Lefschetz number of an involution on the space of harmonic cusp forms ofSL 3. Invent. Math.73, 189–239 (1983)

    Google Scholar 

  30. Matsumoto, H.: Fonctions spheriques sur un groupe semisimplep-adique. C.R. Acad. Sci. Paris269, 829–832 (1969)

    Google Scholar 

  31. Millson J.J.: On the first Betti number of a constant negatively curved manifold. Ann. Math.104, 235–247 (1976)

    Google Scholar 

  32. Rohlfs, J.: On the cuspidal cohomology of the Bianchi modular groups. Math. Z.188, 253–269 (1985)

    Google Scholar 

  33. Rohlfs, J., Speh, B.: Representations with cohomology in the discrete spectrum of subgroups ofSO(n,1) (ℤ) and Lefschetz numbers. Preprint 1985

  34. Silberger, A.J.: Isogeny retrictions of irreducible representations are finite direct sums of irreducible admissible representations. Proc. AMS73, 263–264 (1979)

    Google Scholar 

  35. Tate, J.: Number theoretic background. In: Proc. Symp. Pure Maths., vol. 33, part 2, pp. 3–26. Providence: AMS 1979

    Google Scholar 

  36. Vogan, D.A., Zuckerman, G.: Unitary representations with non-zero cohomology. Compos. Math.53, 51–90 (1984)

    Google Scholar 

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Labesse, J.P., Schwermer, J. On liftings and cusp cohomology of arithmetic groups. Invent Math 83, 383–401 (1986). https://doi.org/10.1007/BF01388968

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