Högskolan i Skövde

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 sequence of graphs approximating the fractal and the regularized Laplacian determinant on the fractal itself which is defined via help of the spectral zeta function. We then at the end present some concrete examples of this phenomenon.