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

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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].

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Authors and Affiliations

  1. Department of Mathematics, University of Maryland, 20742, College Park, MD, USA

    Scott A. Wolpert

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  1. Scott A. Wolpert
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Communicated by S.-T. Yau

Partially supported by the National Science Foundation and the Institute for Physical Science and Technology, University of Maryland, College Park, MD, USA

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Wolpert, S.A. Asymptotics of the spectrum and the Selberg zeta function on the space of Riemann surfaces. Commun.Math. Phys. 112, 283–315 (1987). https://doi.org/10.1007/BF01217814

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  • DOI: https://doi.org/10.1007/BF01217814

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