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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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.

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

First available in Project Euclid: 3 July 2013

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Zentralblatt MATH identifier

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

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


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.

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