Communications in Mathematical Physics

, Volume 130, Issue 3, pp 581–597 | Cite as

Determinants of Laplace-like operators on Riemann surfaces

  • J. Bolte
  • F. Steiner


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.


Neural Network Statistical Physic Complex System Nonlinear Dynamics Differential Operator 
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  1. 1.
    Polyakov, A. M.: Phys. Lett.103B, 207 and 211 (1981)Google Scholar
  2. 2.
    D'Hoker, E., Phong, D. H.: Nucl. Phys.B269, 205 (1986)Google Scholar
  3. 3.
    D'Hoker, E., Phong, D. H.: Commun. Math. Phys.104, 537 (1986)Google Scholar
  4. 4.
    D'Hoker, E., Phong, D. H.: Rev. Mod. Phys.60, 917 (1988)Google Scholar
  5. 5.
    Gilbert, G.: Nucl. Phys.B277, 102 (1986)Google Scholar
  6. 6.
    Namazie, M. A., Rajeev, S.: Nucl. Phys.B277, 332 (1986)Google Scholar
  7. 7.
    Sarnak, P.: Commun. Math. Phys.110, 113 (1987)Google Scholar
  8. 8.
    Voros, A.: Commun. Math. Phys.110, 439 (1987)Google Scholar
  9. 9.
    Steiner, F.: Phys. Lett.188B, 447 (1987)Google Scholar
  10. 10.
    Alvarez, O.: Nucl. Phys.B216, 125 (1983)Google Scholar
  11. 11.
    Minakshisundaram, S., Pleijel, A.: Can. J. Math.1, 242 (1949)Google Scholar
  12. 11a.
    Minakshisundaram, S.: Can. J. Math.1, 320 (1949)Google Scholar
  13. 12.
    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 1983Google Scholar
  14. 13.
    Gradshteyn, I. S., Ryzhik, I. M.: Tables of integrals, series, and products. New York: Academic Press 1980.Google Scholar
  15. 14.
    Fay, J.: J. Reine Angew. Math.293, 143 (1977)Google Scholar
  16. 15.
    Weisberger, W. I.: Nucl. Phys.B284, 439 (1987)Google Scholar
  17. 16.
    Grosche, C.: Ann. Phys.187, 110 (1988)Google Scholar
  18. 17.
    Oshima, K.: Prog. Theor. Phys.81, 286 (1988)Google Scholar
  19. 17a.
    Oshima, K.: Phys. Rev. D41, 702 (1990)Google Scholar

Copyright information

© Springer-Verlag 1990

Authors and Affiliations

  • J. Bolte
    • 1
  • F. Steiner
    • 1
  1. 1.II. Institut für Theoretische PhysikUniversität HamburgHamburg 50Federal Republic of Germany

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