TY - JOUR
T1 - A note on spectral zeta functions of quantum groups
AU - Kurokawa, Nobushige
AU - Wakayama, Masato
N1 - Funding Information:
The authors thank Masanobu Kaneko for his valuable comment. The research of the paper is supported in part by Grant-in Aid for Scientific Research (B) No.15340012, and by Grant-in Aid for Exploratory Research No.13874004, Japan Society for the Promotion of Science.
PY - 2004/3
Y1 - 2004/3
N2 - We study analytic properties of spectral zeta functions associated to actions of the quantum group SUq(2) such as Z(s, SUq(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, SUq(2)). We further discuss a spectral zeta function Z(s, ℂq[x, y]) associated with the so-called model of the representations of Uq(s-fraktur sign and l-fraktur sign2) and show a presence of its series of "trivial" zeros, which is noteworthy.
AB - We study analytic properties of spectral zeta functions associated to actions of the quantum group SUq(2) such as Z(s, SUq(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, SUq(2)). We further discuss a spectral zeta function Z(s, ℂq[x, y]) associated with the so-called model of the representations of Uq(s-fraktur sign and l-fraktur sign2) and show a presence of its series of "trivial" zeros, which is noteworthy.
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U2 - 10.1142/S0129167X04002181
DO - 10.1142/S0129167X04002181
M3 - Article
AN - SCOPUS:7244243854
VL - 15
SP - 125
EP - 133
JO - International Journal of Mathematics
JF - International Journal of Mathematics
SN - 0129-167X
IS - 2
ER -