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

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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