Open Access
July 2013 Dualities for absolute zeta functions and multiple gamma functions
Nobushige Kurokawa, Hiroyuki Ochiai
Proc. Japan Acad. Ser. A Math. Sci. 89(7): 75-79 (July 2013). DOI: 10.3792/pjaa.89.75


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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Nobushige Kurokawa. Hiroyuki Ochiai. "Dualities for absolute zeta functions and multiple gamma functions." Proc. Japan Acad. Ser. A Math. Sci. 89 (7) 75 - 79, July 2013.


Published: July 2013
First available in Project Euclid: 3 July 2013

zbMATH: 1373.11063
MathSciNet: MR3079293
Digital Object Identifier: 10.3792/pjaa.89.75

Primary: 11M06

Keywords: absolute Hurwitz zeta function , absolute zeta function , Kurokawa tensor product , Multiple gamma function , Multiple sine function

Rights: Copyright © 2013 The Japan Academy

Vol.89 • No. 7 • July 2013
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