The zeta function of the Laplacian on certain fractals

Gregory Derfel, Peter J. Grabner, Fritz Vogl

Research output: Contribution to journalArticlepeer-review

22 Scopus citations


We prove that the zeta function ζΔ of the Laplacian Δ on selfsimilar 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, thereby answering a question posed by J. Kigami and M. Lapidus for this class of fractals.

Original languageEnglish
Pages (from-to)881-897
Number of pages17
JournalTransactions of the American Mathematical Society
Issue number2
StatePublished - 1 Feb 2008


  • Complex dynamics
  • Dirichlet series
  • Fractals
  • Laplace operator
  • Spectral decimation

ASJC Scopus subject areas

  • Mathematics (all)
  • Applied Mathematics


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