The Zeta Function of the Laplacian on Certain Fractals
Gregory Derfel, Peter Grabner, Fritz Vogl
Abstract
We prove that the zeta-function ζΔ of the Laplacian Δ on a self-similar fractals with spectral decimation admits a meromorphic continuation to the whole complex plane. We characterise the poles, compute their residues, and give expressions for some special values of the zeta-function. Furthermore, we discuss the presence of oscillations in the eigenvalue counting function.
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