Abstract
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.
| Original language | English |
|---|---|
| Pages (from-to) | 125-133 |
| Number of pages | 9 |
| Journal | International Journal of Mathematics |
| Volume | 15 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - Mar 1 2004 |
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All Science Journal Classification (ASJC) codes
- Mathematics(all)
Cite this
A note on spectral zeta functions of quantum groups. / Kurokawa, Nobushige; Wakayama, Masato.
In: International Journal of Mathematics, Vol. 15, No. 2, 01.03.2004, p. 125-133.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - A note on spectral zeta functions of quantum groups
AU - Kurokawa, Nobushige
AU - Wakayama, Masato
PY - 2004/3/1
Y1 - 2004/3/1
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.
UR - http://www.scopus.com/inward/record.url?scp=7244243854&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=7244243854&partnerID=8YFLogxK
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 -