The Zeta Function of the Laplacian on Certain Fractals
Spectral Theory
2020-07-27 v2 Complex Variables
Abstract
We prove that the zeta-function of the Laplacian on a self-similar fractals with spectral decimation admits a meromorphic continuation to the whole complex plane. We characterise the poles, compute their residues, and give expressions for some special values of the zeta-function. Furthermore, we discuss the presence of oscillations in the eigenvalue counting function.
Keywords
Cite
@article{arxiv.math/0508315,
title = {The Zeta Function of the Laplacian on Certain Fractals},
author = {Gregory Derfel and Peter Grabner and Fritz Vogl},
journal= {arXiv preprint arXiv:math/0508315},
year = {2020}
}
Comments
Added an unconditional proof for the presence of non-real poles of the zeta-function for the class of fractals under consideration