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Communications in Mathematical Physics

, Volume 156, Issue 1, pp 1–16 | Cite as

The Selberg trace formula for bordered Riemann surfaces

  • J. Bolte
  • F. Steiner
Article

Abstract

A Selberg trace formula is derived for the Laplace-Beltrami operator on bordered Riemann surfaces with Dirichlet or Neumann boundary conditions, respectively, using a construction via the compact double of the surface, for which the standard trace formula is valid. Applications of the trace formula to spectral functions of the Laplace-Beltrami operators are discussed and their functional determinants are explicitly expressed in terms of various Selberg zeta functions. For Selberg's zeta function relevant to the Dirichlet boundary value problem a representation as a Dirichlet series is given, for which we conjecture conditional convergence even within the critical strip for Res>1/2.

Keywords

Neural Network Complex System Nonlinear Dynamics Dirichlet Boundary Quantum Computing 
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Copyright information

© Springer-Verlag 1993

Authors and Affiliations

  • J. Bolte
    • 1
  • F. Steiner
    • 1
  1. 1.II. Institut für Theoretische PhysikUniversität HamburgHamburgGermany

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