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Communications in Mathematical Physics

, Volume 112, Issue 2, pp 283–315 | Cite as

Asymptotics of the spectrum and the Selberg zeta function on the space of Riemann surfaces

  • Scott A. Wolpert
Article

Abstract

LetZ(s, R) be the Selberg zeta function of a compact Riemann surfaceR. We study the behavior ofZ(s, R) asR tends to infinity in the moduli space of stable curves. The main result is an estimate forZ(s, R) valid fors in a neighborhood, depending only on the genus, ofs=1. Our analysis gives an alternate proof of the Belavin-Knizhnik double pole result, [5].

Keywords

Neural Network Statistical Physic Complex System Nonlinear Dynamics Modulus Space 
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Copyright information

© Springer-Verlag 1987

Authors and Affiliations

  • Scott A. Wolpert
    • 1
  1. 1.Department of MathematicsUniversity of MarylandCollege ParkUSA

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