A note on spectral zeta functions of quantum groups

Nobushige Kurokawa, Masato Wakayama

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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
Issue number2
Publication statusPublished - Mar 2004
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • General Mathematics


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