Dualities for absolute zeta functions and multiple gamma functions

Nobushige Kurokawa, Hiroyuki Ochiai

Research output: Contribution to journalArticle

5 Citations (Scopus)

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 languageEnglish
Pages (from-to)75-79
Number of pages5
JournalProceedings of the Japan Academy Series A: Mathematical Sciences
Volume89
Issue number7
DOIs
Publication statusPublished - Jul 1 2013

Fingerprint

Multiple gamma Function
Multiple Sine Function
Riemann zeta function
Normalization
Duality
Hurwitz zeta Function
Tensor Product
Functional equation
Simplicity

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

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

In: Proceedings of the Japan Academy Series A: Mathematical Sciences, Vol. 89, No. 7, 01.07.2013, p. 75-79.

Research output: Contribution to journalArticle

@article{614723b0fa2646e2963f26331580537f,
title = "Dualities for absolute zeta functions and multiple gamma functions",
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.",
author = "Nobushige Kurokawa and Hiroyuki Ochiai",
year = "2013",
month = "7",
day = "1",
doi = "10.3792/pjaa.89.75",
language = "English",
volume = "89",
pages = "75--79",
journal = "Proceedings of the Japan Academy Series A: Mathematical Sciences",
issn = "0386-2194",
publisher = "Japan Academy",
number = "7",

}

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 -