### 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 z_{Γ}(s). especially to obtain the functional equation. We also describe the gamma factor of z_{Γ} (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 language | English |
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Pages (from-to) | 447-466 |

Number of pages | 20 |

Journal | Communications in Mathematical Physics |

Volume | 247 |

Issue number | 2 |

DOIs | |

Publication status | Published - May 1 2004 |

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### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

*Communications in Mathematical Physics*,

*247*(2), 447-466. https://doi.org/10.1007/s00220-004-1065-z

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

Research output: Contribution to journal › Article

*Communications in Mathematical Physics*, vol. 247, no. 2, pp. 447-466. https://doi.org/10.1007/s00220-004-1065-z

}

TY - JOUR

T1 - Higher Selberg zeta functions

AU - Kurokawa, Nobushige

AU - Wakayama, Masato

PY - 2004/5/1

Y1 - 2004/5/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=2942560196&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=2942560196&partnerID=8YFLogxK

U2 - 10.1007/s00220-004-1065-z

DO - 10.1007/s00220-004-1065-z

M3 - Article

VL - 247

SP - 447

EP - 466

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 2

ER -