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Determinants of Laplacians

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Abstract

The determinant of the Laplacian on spinor fields on a Riemann surface is evaluated in terms of the value of the Selberg zeta function at the middle of the critical strip. A key role in deriving this relation is played by the Barnes double gamma function.

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Authors and Affiliations

  1. Mathematics Department, Stanford University, 94305, Stanford, CA, USA

    Peter Sarnak

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  1. Peter Sarnak
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Additional information

Communicated by B. Simon

This work was supported in part by the NSF Grant No. DMS-85-04329

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Sarnak, P. Determinants of Laplacians. Commun.Math. Phys. 110, 113–120 (1987). https://doi.org/10.1007/BF01209019

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  • DOI: https://doi.org/10.1007/BF01209019

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