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We investigate the existence of the meromorphic extension of the spectral zeta function of the Laplacian on self-similar fractals using the classical results of Kigami and Lapidus (based on the renewal theory) and new results of Hambly and Kajino based on the heat kernel estimates and other probabilistic techniques.
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Fractal geometry, complex dimensions and zeta functions
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Uniqueness of Brownian motion on Sierpiński carpets
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2013
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