Skip to main content
SpringerLink
Log in

Determinants of Laplace-like operators on Riemann surfaces

  • Published:
Communications in Mathematical Physics Aims and scope Submit manuscript

Abstract

We calculate determinants of second order partial differential operators defined on Riemann surfaces of genus greater than one using a relation between Selberg's zeta function and functional determinants. In addition, we perform a calculation of these determinants directly using Selberg's trace formula, and compare our results with previous computations which followed the latter route.

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

Similar content being viewed by others

References

  1. Polyakov, A. M.: Phys. Lett.103B, 207 and 211 (1981)

    Google Scholar 

  2. D'Hoker, E., Phong, D. H.: Nucl. Phys.B269, 205 (1986)

    Google Scholar 

  3. D'Hoker, E., Phong, D. H.: Commun. Math. Phys.104, 537 (1986)

    Google Scholar 

  4. D'Hoker, E., Phong, D. H.: Rev. Mod. Phys.60, 917 (1988)

    Google Scholar 

  5. Gilbert, G.: Nucl. Phys.B277, 102 (1986)

    Google Scholar 

  6. Namazie, M. A., Rajeev, S.: Nucl. Phys.B277, 332 (1986)

    Google Scholar 

  7. Sarnak, P.: Commun. Math. Phys.110, 113 (1987)

    Google Scholar 

  8. Voros, A.: Commun. Math. Phys.110, 439 (1987)

    Google Scholar 

  9. Steiner, F.: Phys. Lett.188B, 447 (1987)

    Google Scholar 

  10. Alvarez, O.: Nucl. Phys.B216, 125 (1983)

    Google Scholar 

  11. Minakshisundaram, S., Pleijel, A.: Can. J. Math.1, 242 (1949)

    Google Scholar 

  12. Minakshisundaram, S.: Can. J. Math.1, 320 (1949)

    Google Scholar 

  13. Hejhal, D. A.: The Selberg trace formula forPSL(2,R), vol. I. Lecture Notes in Mathematics, vol. 548. Berlin, Heidelberg, New York: Springer 1976, vol. II. Lecture Notes in Mathematics, vol. 1001. Berlin, Heidelberg, New York: Springer 1983

    Google Scholar 

  14. Gradshteyn, I. S., Ryzhik, I. M.: Tables of integrals, series, and products. New York: Academic Press 1980.

    Google Scholar 

  15. Fay, J.: J. Reine Angew. Math.293, 143 (1977)

    Google Scholar 

  16. Weisberger, W. I.: Nucl. Phys.B284, 439 (1987)

    Google Scholar 

  17. Grosche, C.: Ann. Phys.187, 110 (1988)

    Google Scholar 

  18. Oshima, K.: Prog. Theor. Phys.81, 286 (1988)

    Google Scholar 

  19. Oshima, K.: Phys. Rev. D41, 702 (1990)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. II. Institut für Theoretische Physik, Universität Hamburg, Luruper Chaussee 149, D-2000, Hamburg 50, Federal Republic of Germany

    J. Bolte & F. Steiner

Authors
  1. J. Bolte
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. F. Steiner
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Communicated by S.-T. Yau

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bolte, J., Steiner, F. Determinants of Laplace-like operators on Riemann surfaces. Commun.Math. Phys. 130, 581–597 (1990). https://doi.org/10.1007/BF02096935

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02096935

Keywords

Search

Navigation