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A NOTE ON SPECTRAL ZETA FUNCTIONS OF QUANTUM GROUPS

NOBUSHIGE KUROKAWA

Department of Mathematics, Tokyo Institute of Technology, Oh-okayama Meguro-ku, Tokyo, 152-8550, Japan

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and

MASATO WAKAYAMA

Faculty of Mathematics, Kyushu University, Hakozaki Higashi-ku, Fukuoka, 812-8581, Japan

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https://doi.org/10.1142/S0129167X04002181Cited by:0 (Source: Crossref)

Abstract

We study analytic properties of spectral zeta functions associated to actions of the quantum group SU_q(2) such as Z(s, SU_q(2)), the zeta function corresponding to the regular representation introduced in [15]. As an application, we show the special value ζ(3) of the Riemann zeta function ζ(s) is given in terms of the classical limit of Z(s, SU_q(2)). We further discuss a spectral zeta function associated with the so-called model of the representations of and show a presence of its series of "trivial" zeros, which is noteworthy.

Keywords:

AMSC: 11M36, 17B37, 20G42

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