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A connection between discrete and regularized Laplacian determinants on fractals

A connection between discrete and regularized Laplacian determinants on fractals

Abstract The spectral zeta function of the Laplacian on self-similar fractal sets has been previously studied and shown to meromorphically extend to the complex plane. In this work we establish that under certain conditions a relationship exists between the logarithm of the determinant of the discrete graph Laplacian on the …