Regularized Laplacian Determinants of Self-similar Fractals
نویسنده
چکیده
We study the spectral zeta functions of the Laplacian on self-similar fractals. These functions are known to meromorphically extend to the entire complex plane, and the locations of their poles, sometimes referred to as complex dimensions, are of special interest. We give examples of self-similar sets such that their complex dimensions are not on the imaginary axis, which allows us to interpret their Laplacian determinant as the regularized product of their eigenvalues. We then investigate a connection between the logarithm of the determinant of the discrete graph Laplacian and the regularized one.
منابع مشابه
Self-similar fractals and arithmetic dynamics
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