Higher Selberg zeta functions

Nobushige Kurokawa, Masato Wakayama

Research output: Contribution to journalArticle

10 Citations (Scopus)

Abstract

In the paper [KW2] we introduced a new type of Selberg zeta function for establishing a certain identity among the non-trivial zeroes of the Selberg zeta function and of the Riemann zeta function. We shall call this zeta function a higher Selberg zeta function. The purpose of this paper is to study the analytic properties of the higher Selberg zeta function zΓ(s). especially to obtain the functional equation. We also describe the gamma factor of zΓ (s) in terms of the triple sine function explicitly and, further, determine the complete higher Selberg zeta function with having a discussion of a certain generalized zeta regularization.

Original languageEnglish
Pages (from-to)447-466
Number of pages20
JournalCommunications in Mathematical Physics
Volume247
Issue number2
DOIs
Publication statusPublished - May 1 2004

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Selberg zeta Function
Riemann zeta function
Functional equation
Regularization
Zero

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

Higher Selberg zeta functions. / Kurokawa, Nobushige; Wakayama, Masato.

In: Communications in Mathematical Physics, Vol. 247, No. 2, 01.05.2004, p. 447-466.

Research output: Contribution to journalArticle

Kurokawa, Nobushige ; Wakayama, Masato. / Higher Selberg zeta functions. In: Communications in Mathematical Physics. 2004 ; Vol. 247, No. 2. pp. 447-466.
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