Milnor-Selberg zeta functions and zeta regularizations

Nobushige Kurokawa, Masato Wakayama, Yoshinori Yamasaki

Research output: Contribution to journalArticle

Abstract

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
Volume64
Issue number1
DOIs
Publication statusPublished - Feb 1 2013

Fingerprint

Selberg zeta Function
determinants
gamma function
Regularization
Determinant
Multiple gamma Function
Euler Product
Gamma function
Analytic Continuation
products
Riemann Surface
Functional equation
Genus

All Science Journal Classification (ASJC) codes

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

Cite this

Milnor-Selberg zeta functions and zeta regularizations. / Kurokawa, Nobushige; Wakayama, Masato; Yamasaki, Yoshinori.

In: Journal of Geometry and Physics, Vol. 64, No. 1, 01.02.2013, p. 120-145.

Research output: Contribution to journalArticle

Kurokawa, Nobushige ; Wakayama, Masato ; Yamasaki, Yoshinori. / Milnor-Selberg zeta functions and zeta regularizations. In: Journal of Geometry and Physics. 2013 ; Vol. 64, No. 1. pp. 120-145.
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