A note on spectral zeta functions of quantum groups

Nobushige Kurokawa, Masato Wakayama

Research output: Contribution to journalArticle

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 languageEnglish
Pages (from-to)125-133
Number of pages9
JournalInternational Journal of Mathematics
Volume15
Issue number2
DOIs
Publication statusPublished - Mar 1 2004

Fingerprint

Spectral Function
Quantum Groups
Riemann zeta function
Classical Limit
Trivial
Series
Zero
Model

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 journalArticle

@article{dd8da7dbb00b4db48ec72f9a4ee32d68,
title = "A note on spectral zeta functions of quantum groups",
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.",
author = "Nobushige Kurokawa and Masato Wakayama",
year = "2004",
month = "3",
day = "1",
doi = "10.1142/S0129167X04002181",
language = "English",
volume = "15",
pages = "125--133",
journal = "International Journal of Mathematics",
issn = "0129-167X",
publisher = "World Scientific Publishing Co. Pte Ltd",
number = "2",

}

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 -