### 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 |

### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics

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## Cite this

Kurokawa, N., & Wakayama, M. (2004). Higher Selberg zeta functions.

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