Remote Access Bulletin of the American Mathematical Society

Bulletin of the American Mathematical Society

ISSN 1088-9485(online) ISSN 0273-0979(print)

 

 

On the Selberg trace formula in the case of compact quotient


Author: Nolan R. Wallach
Journal: Bull. Amer. Math. Soc. 82 (1976), 171-195
MSC (1970): Primary 10D20, 22E40, 43A15
MathSciNet review: 0404533
Full-text PDF

References | Similar Articles | Additional Information

References [Enhancements On Off] (What's this?)

  • 1. James Arthur, The trace formula for reductive groups, Conference on automorphic theory (Dijon, 1981) Publ. Math. Univ. Paris VII, vol. 15, Univ. Paris VII, Paris, 1983, pp. 1–41. MR 723181, 10.1007/978-1-4684-6730-7_1
  • 2. Armand Borel, Introduction to automorphic forms, Algebraic Groups and Discontinuous Subgroups (Proc. Sympos. Pure Math., Boulder, Colo., 1965) Amer. Math. Soc., Providence, R.I., 1966, pp. 199–210. MR 0207650
  • 3. Armand Borel, Introduction aux groupes arithmétiques, Publications de l’Institut de Mathématique de l’Université de Strasbourg, XV. Actualités Scientifiques et Industrielles, No. 1341, Hermann, Paris, 1969 (French). MR 0244260
  • 4. Michel Duflo and Jean-Pierre Labesse, Sur la formule des traces de Selberg, Ann. Sci. École Norm. Sup. (4) 4 (1971), 193–284. MR 0437462
  • 5. N. Dunford and J. Schwartz, Linear operators. Vol. 3, Interscience, New York, 1972.
  • 6. R. Gangolli, Asymptotic behavior of spectra of compact quotients of certain symmetric spaces, Acta Math. 121 (1968), 151–192. MR 0239000
  • 7. R. Gangolli, On the Plancherel formula and the Paley-Wiener theorem for spherical functions on semisimple Lie groups, Ann. of Math. (2) 93 (1971), 150–165. MR 0289724
  • 8. I. M. Gel′fand, Automorphic functions and the theory of representations, Proc. Internat. Congr. Mathematicians (Stockholm, 1962) Inst. Mittag-Leffler, Djursholm, 1963, pp. 74–85. MR 0175997
  • 9. I. M. Gel′fand, M. I. Graev, and I. I. Pjateckiĭ-Šapiro, Teoriya predstavlenii i avtomorfnye funktsii, Generalized functions, No. 6, Izdat. “Nauka”, Moscow, 1966 (Russian). MR 0220673
  • 10. Harish-Chandra, Representations of semisimple Lie groups. VI. Integrable and square-integrable representations, Amer. J. Math. 78 (1956), 564–628. MR 0082056
  • 11. Harish-Chandra, Spherical functions on a semi-simple Lie group. I, II, Amer. J. Math. 80 (1958), 241-310, 553-613. MR 20 #925; 21 #92.
  • 12. Harish-Chandra, Automorphic forms on semi-simple Lie groups, Lecture Notes in Math., no. 62, Springer-Verlag, New York and Berlin, 1968. MR 38 #1216.
  • 13. Harish-Chandra, Discrete series for semisimple Lie groups. II. Explicit determination of the characters, Acta Math. 116 (1966), 1–111. MR 0219666
  • 14. Harish-Chandra, On the theory of the Eisenstein integral, Conference on Harmonic Analysis (Univ. Maryland, College Park, Md., 1971), Springer, Berlin, 1972, pp. 123–149. Lecture Notes in Math., Vol. 266. MR 0399355
  • 15. Sigurđur Helgason, Differential geometry and symmetric spaces, Pure and Applied Mathematics, Vol. XII, Academic Press, New York-London, 1962. MR 0145455
  • 16. Sigurđur Helgason, An analogue of the Paley-Wiener theorem for the Fourier transform on certain symmetric spaces, Math. Ann. 165 (1966), 297–308. MR 0223497
  • 17. R. Hotta and R. Parthasarathy, Multiplicity formulae for discrete series, Invent. Math. 26 (1974), 133–178. MR 0348041
  • 18. Ryoshi Hotta and Nolan R. Wallach, On Matsushima’s formula for the Betti numbers of a locally symmetric space, Osaka J. Math. 12 (1975), no. 2, 419–431. MR 0379756
  • 19. K. Johnson, Paley-Wiener theorems for rank one groups (to appear).
  • 20. H. Johnson and N. R. Wallach, Intertwining operators and composition series for the spherical principal series. I, Trans. Amer. Math. Soc. (to appear).
  • 21. D. A. Každan, On the connection of the dual space of a group with the structure of its closed subgroups, Funkcional. Anal. i Priložen. 1 (1967), 71–74 (Russian). MR 0209390
  • 22. A. W. Knapp and E. M. Stein, Intertwining operators for semisimple groups, Ann. of Math. (2) 93 (1971), 489–578. MR 0460543
  • 23. Shoshichi Kobayashi and Katsumi Nomizu, Foundations of differential geometry. Vol. II, Interscience Tracts in Pure and Applied Mathematics, No. 15 Vol. II, Interscience Publishers John Wiley & Sons, Inc., New York-London-Sydney, 1969. MR 0238225
  • 24. Bertram Kostant, On the existence and irreducibility of certain series of representations, Bull. Amer. Math. Soc. 75 (1969), 627–642. MR 0245725, 10.1090/S0002-9904-1969-12235-4
  • 25. R. P. Langlands, Dimension of spaces of automorphic forms, Algebraic Groups and Discontinuous Subgroups (Proc. Sympos. Pure Math., Boulder, Colo., 1965) Amer. Math. Soc., Providence, R.I., 1966, pp. 253–257. MR 0212135
  • 26. Yozô Matsushima, On the first Betti number of compact quotient spaces of higher-dimensional symmetric spaces, Ann. of Math. (2) 75 (1962), 312–330. MR 0158406
  • 27. Yozô Matsushima, A formula for the Betti numbers of compact locally symmetric Riemannian manifolds, J. Differential Geometry 1 (1967), 99–109. MR 0222908
  • 28. H. P. McKean Jr. and I. M. Singer, Curvature and the eigenvalues of the Laplacian, J. Differential Geometry 1 (1967), no. 1, 43–69. MR 0217739
  • 29. G. D. Mostow, Strong rigidity of locally symmetric spaces, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1973. Annals of Mathematics Studies, No. 78. MR 0385004
  • 30. M. S. Raghunathan, Discrete subgroups of Lie groups, Springer-Verlag, New York-Heidelberg, 1972. Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 68. MR 0507234
  • 31. Paul J. Sally Jr., Analytic continuation of the irreducible unitary representations of the universal covering group of 𝑆𝐿(2,𝑅), Memoirs of the American Mathematical Society, No. 69, American Mathematical Society, Providence, R. I., 1967. MR 0235068
  • 32. Wilfried Schmid, On a conjecture of Langlands, Ann. of Math. (2) 93 (1971), 1–42. MR 0286942
  • 33. Jean-Pierre Serre, Cohomologie des groupes discrets, Prospects in mathematics (Proc. Sympos., Princeton Univ., Princeton, N.J., 1970) Princeton Univ. Press, Princeton, N.J., 1971, pp. 77–169. Ann. of Math. Studies, No. 70 (French). MR 0385006
  • 34. È. B. Vinberg, Some examples of crystallographic groups in Lobačevskiĭ spaces, Mat. Sb. (N.S.) 78 (120) (1969), 633–639 (Russian). MR 0246193
  • 35. Nolan R. Wallach, Harmonic analysis on homogeneous spaces, Marcel Dekker, Inc., New York, 1973. Pure and Applied Mathematics, No. 19. MR 0498996
  • 36. Nolan R. Wallach, An asymptotic formula of Gelfand and Gangolli for the spectrum of 𝐺\𝐺, J. Differential Geometry 11 (1976), no. 1, 91–101. MR 0417340
  • 37. Garth Warner, Harmonic analysis on semi-simple Lie groups. I, Springer-Verlag, New York-Heidelberg, 1972. Die Grundlehren der mathematischen Wissenschaften, Band 188. MR 0498999
  • 38. E. T. Whittaker and G. N. Watson, A course of modern analysis, Cambridge Mathematical Library, Cambridge University Press, Cambridge, 1996. An introduction to the general theory of infinite processes and of analytic functions; with an account of the principal transcendental functions; Reprint of the fourth (1927) edition. MR 1424469
  • 39. James Morrow and Kunihiko Kodaira, Complex manifolds, Holt, Rinehart and Winston, Inc., New York-Montreal, Que.-London, 1971. MR 0302937

Similar Articles

Retrieve articles in Bulletin of the American Mathematical Society with MSC (1970): 10D20, 22E40, 43A15

Retrieve articles in all journals with MSC (1970): 10D20, 22E40, 43A15


Additional Information

DOI: https://doi.org/10.1090/S0002-9904-1976-13979-1