Proceedings of the Japan Academy, Series A, Mathematical Sciences

Dualities for absolute zeta functions and multiple gamma functions

Nobushige Kurokawa and Hiroyuki Ochiai

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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.

Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 89, Number 7 (2013), 75-79.

Dates
First available in Project Euclid: 3 July 2013

Permanent link to this document
https://projecteuclid.org/euclid.pja/1372859300

Digital Object Identifier
doi:10.3792/pjaa.89.75

Mathematical Reviews number (MathSciNet)
MR3079293

Zentralblatt MATH identifier
1373.11063

Subjects
Primary: 11M06: $\zeta (s)$ and $L(s, \chi)$

Keywords
Absolute zeta function multiple gamma function multiple sine function absolute Hurwitz zeta function Kurokawa tensor product

Citation

Kurokawa, Nobushige; Ochiai, Hiroyuki. Dualities for absolute zeta functions and multiple gamma functions. Proc. Japan Acad. Ser. A Math. Sci. 89 (2013), no. 7, 75--79. doi:10.3792/pjaa.89.75. https://projecteuclid.org/euclid.pja/1372859300


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