Skip to main content
SpringerLink
Log in

A factorization of the selberg zeta function attached to a rank 1 space form

  • Published:
manuscripta mathematica Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  1. L. Alvarez-Gaume', G. Moore, C. Vafa, Theta functions, modular invariance, and strings,Comm. Math. Physics 106 (1986), 1–40

    Article  MathSciNet  Google Scholar 

  2. E. Barnes, The theory of theG-functions,Quarterly J. of Math 31 (1900), 264–314

    MATH  Google Scholar 

  3. E. D'Hoker, D. Phong, On determinants of Laplacians on Riemann surfaces,Comm. Math. Physics 104 (1986), 537–545

    Article  MATH  MathSciNet  Google Scholar 

  4. I. Efrat, Determinants of Laplacians on surfaces of finite volume,Comm. Math. Physics 119 (1988), 443–451

    Article  MATH  MathSciNet  Google Scholar 

  5. J. Fischer, An approach to the Selberg trace formula via the Selberg zeta function,Lecture Notes in Math. 1253 (1987), Springer-Verlag

  6. D. Fried, The zeta function of Ruelle and Selberg I,Ann. École Norm. Sup., 19 (1986), 491–517

    MATH  MathSciNet  Google Scholar 

  7. D. Fried, Analytic torsion and closed geodesics on hyperbolic manifolds,Inven. Math. 84 (1986), 523–540

    Article  MATH  MathSciNet  Google Scholar 

  8. A. Fujii, N. Kurokawa, T. Sunada, editors, Zeta Functions in Geometry, Proceedings of the August, 1990 Conference (Tokyo Institute of Tech.); to appear in Advanced Studies in Pure Math. series, Academic Press

  9. R. Gangolli, Zeta functions of Selberg's type for compact space forms of symmetric spaces of rank one,Ill. J. Math. 21 (1977), 1–42

    MATH  MathSciNet  Google Scholar 

  10. R. Gangolli, G. Warner, Zeta functions of Selberg's type for some noncompact quotients of symmetric spaces of rank one,Nagoya Math. J. 78 (1980), 1–44

    MathSciNet  Google Scholar 

  11. I. Gradshteyn, I. Ryzhik, Table of integrals, series, and products, corrected and enlarged edition prepared by A. Jeffrey (1965), 6th printing, Academic Press

  12. Harish-Chandra, Spherical functions on a semisimple Lie group I, II,Am. J. Math. 80 (1958), 241–310, 553–613

    Article  MathSciNet  Google Scholar 

  13. M. Kielanczyk, Determinant of Laplacians, Ph.D. thesis, M.I.T. 1986

  14. Kinkelin, J. ReineAngew Math. (Crelle)57 (1860), 122–138

    Article  MATH  Google Scholar 

  15. S, Koyama, The Selberg zeta function and Omthe determinant of the Laplacian,Proc. Japan Acad. 65 (1989), 280–283

    Article  MATH  MathSciNet  Google Scholar 

  16. S. Koyama, Determinant expression of Selberg zeta functions I,Trans. Am. Math. Soc. 324 (1991), 149–168

    Article  MATH  MathSciNet  Google Scholar 

  17. S, Koyama, Determinant expression of Selberg zeta functions II, III, (1990) reprints

  18. N. Kurokawa, Parabolic components of zeta functions,Proc. Japan Acad. 64 (1988), 21–24

    MATH  MathSciNet  Google Scholar 

  19. R. Miatello, On the Plancherel measure for linear Lie groups of rank one,Manuscripta Math. 29 (1979), 249–276

    Article  MATH  MathSciNet  Google Scholar 

  20. S. Minakshisundaram, A. Pleijel, Some properties of the eigenfunctions of the Laplace operator on Riemannian manifolds,Canadian J. Math. 1 (1949), 242–256

    MATH  MathSciNet  Google Scholar 

  21. K. Okamoto, On the Plancherel formula for some types of simple Lie groups,Osaka J. Math. 2 (1965), 247–282

    MATH  MathSciNet  Google Scholar 

  22. A. Polyakov, Quantum geometry of bosonic strings,Physics Letters 103 B (1981), 207–210

    Article  MathSciNet  Google Scholar 

  23. P. Sarnak, Determinants of Laplacians,Comm. Math. Physics 110 (1987), 113–120.

    Article  MATH  MathSciNet  Google Scholar 

  24. P. Sarnak, Special valves of Selberg's zeta function, from Number Theory, Trace Formula and Discrete Groups, 1987 Symposium in Honor of Atle Selberg (Oslo, Norway), 457–465

  25. P. Sarnak, Determinant of Laplacians; heights and finiteness, 1989 preprint.

  26. A. Selberg, Harmonic analysis on discontinuous groups in weakly symmetric Riemannian space with applications to Dirichlet series,J. Indian Math. Math. Soc. 20 (1956), 47–87

    MathSciNet  MATH  Google Scholar 

  27. M-F. Vignéras, L'equation fonctionelle de la fonction zêta de Selberg du group modulaire PSL (2,Z), Société Arithmétique de France,Asterérisque 61 (1979), 235–249

    MATH  Google Scholar 

  28. A. Voros, Spectral functions, special functions and the Selberg zeta function,Comm. Math. Physics 110 (1987), 439–465

    Article  MATH  MathSciNet  Google Scholar 

  29. M. Wakayama, Zeta function of Selberg's type associated with homogeneous vector bundles,Horoshima Math. 15 (1985), 235–295

    MATH  MathSciNet  Google Scholar 

  30. E. Whittaker, G. Watson, A Course of Modern Analysis, 4th ed. (1927), Cambridge Univ. Press, London and New York

    MATH  Google Scholar 

  31. F. Williams, Formula for the class 1 spectrum and the meromorphic continuation of Minakshisundaram-Pleijel series, 1989 preprint now being rewritten

  32. F. Williams, Some zeta functions attached to Φ⊃G/K, a paper presented at the 3rd workshop on Representation Theory of Lie Groups and its Applications (Carlos Paz, Argentina) (1989); to appear in a volume on the proceedings of the workshop Birkhäuser Pub

  33. F. Williams, Lectures on the spectrum ofL 2(Φ⊃G), Pitman Research Notes in Math. Series 242 (1991), Longman House Pub

  34. F. Williams, On certain definite integrals which arise in automorphic Lie theory, 1991 manuscript

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Massachusetts, 01003, Amherst, Massachusetts

    Floyd L. Williams

Authors
  1. Floyd L. Williams
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Williams, F.L. A factorization of the selberg zeta function attached to a rank 1 space form. Manuscripta Math 77, 17–39 (1992). https://doi.org/10.1007/BF02567041

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02567041

Keywords

Search

Navigation