Abstract
We study theoretically and numerically the role of the fluctuations of eigenvalue spectra {itμn in a particular analytical continuation process applied to the (generalized) zeta functionZ(s)=∑ n μ −sn fors large and positive. A particularly interesting example is the spectrum of the Laplacian on a triangular domain which tessellates a compact surface of constant negative curvature (of genus two). We indeed find that the fluctuations restrict the abscissa of convergence, and also affect the rate of convergence. This then initiates a new approach to the exploration of spectral fluctuations through the convergence of analytical continuation processes.
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work done while at the Service de Physique Théorique, Saclay, and Institut de Physique Nucléaire, Orsay.
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Balazs, N.L., Schmit, C. & Voros, A. Spectral fluctuations and zeta functions. J Stat Phys 46, 1067–1090 (1987). https://doi.org/10.1007/BF01011157
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DOI: https://doi.org/10.1007/BF01011157