Milnor-Selberg zeta functions and zeta regularizations

Nobushige Kurokawa, Masato Wakayama, Yoshinori Yamasaki

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


By a similar idea for the construction of Milnor's gamma functions, we introduce "higher depth determinants" of the Laplacian on a compact Riemann surface of genus greater than one. We prove that, as a generalization of the determinant expression of the Selberg zeta function, this higher depth determinant can be expressed as a product of multiple gamma functions and what we call a Milnor-Selberg zeta function. It is shown that the Milnor-Selberg zeta function admits an analytic continuation, a functional equation and, remarkably, has an Euler product.

Original languageEnglish
Pages (from-to)120-145
Number of pages26
JournalJournal of Geometry and Physics
Issue number1
Publication statusPublished - Feb 2013
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Mathematical Physics
  • Physics and Astronomy(all)
  • Geometry and Topology


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