Inventiones mathematicae

, Volume 105, Issue 1, pp 185–216 | Cite as

R-torsion and zeta functions for locally symmetric manifolds

  • Henri Moscovici
  • Robert J. Stanton


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [B-M] Barbasch, D., Moscovici, H.:L 2-index and the Selberg trace formula. J. Funct. Anal.53, 151–201 (1983)Google Scholar
  2. [B-W] Borel, A., Wallach, N.: Continuous cohomology, discrete subgroups, and representations of reductive groups. Ann. Math. Stud.94, 1–387 (1980)Google Scholar
  3. [C] Cheeger, J.: Analytic torsion and the heat equation. Ann. Math.109, 259–322 (1979)Google Scholar
  4. [D-K-V] Duistermaat, J.J., Kolk, J.A.C., Varadarajan, V.S.: Spectra of compact locally symmetric manifolds of negative curvature. Invent. Math.52, 27–93 (1979)Google Scholar
  5. [E] Eberlein, P.: A canonical form for compact nonpositively curved manifolds whose fundamental groups have nontrivial center. Math. Ann.260, 23–29 (1982)Google Scholar
  6. [F1] Fried, D.: Lefschetz formulas for flows. In: Verjovsky A. (ed.) The Lefschetz Centennial Conference, Part III. Contemp. Mathematics, vol.58 Providence: Am. Math. Soc. 1987Google Scholar
  7. [F2] Fried, D.: Counting circles.Dynamical Systems. (Lect. Notes Math., vol.1342, pp. 196–215 Berlin Heidelberg New York, Springer 1988Google Scholar
  8. [F3] Fried, D.: Analytic torsion and closed geodesics on hyperbolic manifolds. Invent. Math.84, 523–540 (1986)Google Scholar
  9. [G-S] Günther, P., Schimming, R.: Curvature and Spectrum of Compact Riemannian manifolds. J. Differ. Geometry12, 599–618 (1977)Google Scholar
  10. [H] Haefliger, A.: Groupoids d'holonomie et classifiants,Structure transverse des feuilletages. Astérisque116, 70–97 (1984)Google Scholar
  11. [H-C;I] Harish-Chandra: Harmonic analysis on real reductive groups, I. J. Funct. Anal.19, 104–204 (1975)Google Scholar
  12. [H-C;III] Harish-Chandra: Harmonic analysis on real reductive groups, III. The Maass-Selberg relations and the Plancherel formula. Ann. Math.104, 117–201 (1976)Google Scholar
  13. [H-C; DSII] Harish-Chandra: Discrete series for semisimple Lie groups, II. Acta Math.116, 1–111 (1966)Google Scholar
  14. [H-C; S] Harish-Chandra: Supertempered distributions on real reductive groups. Adv. Math., Suppl. Stud.8, 139–153 (1983)Google Scholar
  15. [H-P] Hotta, R., Parthasarathy, R.: A geometric meaning of the multiplicity of integrable discrete classes inL 2(Γ \G). Osaka J. Math.10, 211–234 (1973)Google Scholar
  16. [M] Milnor, J.: Infinite cyclic coverings. In: Conf. on the Topology of Manifolds, pp. 115–133, Boston: Prindle, Weber & Schmidt 1968Google Scholar
  17. [M-S] Moscovici, H., Stanton, R.J.: Eta invariants of Dirac operators on locally symmetric manifolds. Invent. Math.95, 629–666 (1989)Google Scholar
  18. [M-S,2] Moscovici, H., Stanton, R.J.: Holomorphic torsion for Hermitian locally symmetric manifolds. (in preparation)Google Scholar
  19. [Mu] Müller, W.: Analytic torsion andR-torsion of Riemannian manifolds, Adv. Math. Suppl. Stud.28, 233–305 (1978)Google Scholar
  20. [R-S1] Ray, D.B., Singer, I.:R-torsion and the Laplacian on Riemannian manifolds. Adv. Math. Suppl. Stud.7, 145–210 (1971)Google Scholar
  21. [R-S2] Ray, D.B., Singer, I.: Analytic torsion for complex manifolds. Ann. Math.98, 154–177 (1973)Google Scholar
  22. [Sc] Schmid, W.: On a conjecture of Langlands, Ann. Math.93, 1–42 (1971)Google Scholar
  23. [S] Schwartz, L.: Théorie des distributions. Paris: Hermann 1966Google Scholar
  24. [Se] Selberg, A.: Harmonic analysis and discontinuous groups in weakly symmetric Riemannian spaces with applications to Dirichlet series. J. Indian Math. Soc.20, 47–87 (1956)Google Scholar
  25. [V] Voros, A.: Spectral functions, special functions and the Selberg zeta function. Commun. Math. Phys.110, 439–465 (1987)Google Scholar
  26. [W] Wallach, N.R.: On the Selberg trace formula in the case of compact quotient. Bull. Am. Math. Soc.82, 171–195 (1976)Google Scholar

Copyright information

© Springer International 1991

Authors and Affiliations

  • Henri Moscovici
    • 1
  • Robert J. Stanton
    • 1
  1. 1.Department of MathematicsOhio State UniversityColumbusUSA

Personalised recommendations