English

A connection between discrete and regularized Laplacian determinants on fractals

Spectral Theory 2023-12-25 v1

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 under certain conditions a relationship between the logarithm of the determinant of the discrete graph Laplacian on the sequence of graphs approximating the fractal and the regularized determinant which is defined via help of the spectral zeta function. We then at the end present some concrete examples of this phenomenon.

Keywords

Cite

@article{arxiv.2312.14802,
  title  = {A connection between discrete and regularized Laplacian determinants on fractals},
  author = {Konstantinos Tsougkas},
  journal= {arXiv preprint arXiv:2312.14802},
  year   = {2023}
}

Comments

19 pages

R2 v1 2026-06-28T14:00:02.440Z