### Abstract

We study absolute zeta functions from the view point of a canonical normalization. We introduce the absolute Hurwitz zeta function for the normalization. In particular, we show that the theory of multiple gamma and sine functions gives good normalizations in cases related to the Kurokawa tensor product. In these cases, the functional equation of the absolute zeta function turns out to be equivalent to the simplicity of the associated non-classical multiple sine function of negative degree.

Original language | English |
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Pages (from-to) | 75-79 |

Number of pages | 5 |

Journal | Proceedings of the Japan Academy Series A: Mathematical Sciences |

Volume | 89 |

Issue number | 7 |

DOIs | |

Publication status | Published - Jul 1 2013 |

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### All Science Journal Classification (ASJC) codes

- Mathematics(all)

### Cite this

**Dualities for absolute zeta functions and multiple gamma functions.** / Kurokawa, Nobushige; Ochiai, Hiroyuki.

Research output: Contribution to journal › Article

*Proceedings of the Japan Academy Series A: Mathematical Sciences*, vol. 89, no. 7, pp. 75-79. https://doi.org/10.3792/pjaa.89.75

}

TY - JOUR

T1 - Dualities for absolute zeta functions and multiple gamma functions

AU - Kurokawa, Nobushige

AU - Ochiai, Hiroyuki

PY - 2013/7/1

Y1 - 2013/7/1

N2 - We study absolute zeta functions from the view point of a canonical normalization. We introduce the absolute Hurwitz zeta function for the normalization. In particular, we show that the theory of multiple gamma and sine functions gives good normalizations in cases related to the Kurokawa tensor product. In these cases, the functional equation of the absolute zeta function turns out to be equivalent to the simplicity of the associated non-classical multiple sine function of negative degree.

AB - We study absolute zeta functions from the view point of a canonical normalization. We introduce the absolute Hurwitz zeta function for the normalization. In particular, we show that the theory of multiple gamma and sine functions gives good normalizations in cases related to the Kurokawa tensor product. In these cases, the functional equation of the absolute zeta function turns out to be equivalent to the simplicity of the associated non-classical multiple sine function of negative degree.

UR - http://www.scopus.com/inward/record.url?scp=84880648636&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84880648636&partnerID=8YFLogxK

U2 - 10.3792/pjaa.89.75

DO - 10.3792/pjaa.89.75

M3 - Article

AN - SCOPUS:84880648636

VL - 89

SP - 75

EP - 79

JO - Proceedings of the Japan Academy Series A: Mathematical Sciences

JF - Proceedings of the Japan Academy Series A: Mathematical Sciences

SN - 0386-2194

IS - 7

ER -