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The spectral zeta function of the Laplacian on self-similar fractal sets hasbeen previously studied and shown to meromorphically extend to the complexplane. In this work we establish under certain conditions a relationshipbetween the logarithm of the determinant of the discrete graph Laplacian on thesequence of graphs approximating the fractal and the regularized determinantwhich is defined via help of the spectral zeta function. We then at the endpresent some concrete examples of this phenomenon.

A connection between discrete and regularized Laplacian determinants on fractals