 04311 Takashi Ichinose and Masato Wakayama
 Zeta functions for the spectrum of the noncommutative
harmonic oscillators
(813K, ps.file)
Sep 30, 04

Abstract ,
Paper (src),
View paper
(auto. generated ps),
Index
of related papers

Abstract. This paper investigates the spectral
zeta function of the noncommutative harmonic oscillator
studied in \cite{PW1, 2}.
It is shown, as one of the basic analytic properties, that
the spectral zeta function is extended to a
meromorphic function in the whole
complex plane with a simple pole at $s=1$, and further that it
has a zero at all nonpositive even integers, i.e. at $s=0$ and at
those negative even integers where
the Riemann zeta function has the socalled trivial zeros.
As a byproduct of the study, both the upper and the lower bounds
are also given for the first eigenvalue of the
noncommutative harmonic oscillator.
 Files:
04311.src(
04311.comments ,
04311.keywords ,
Fzfinal.ps )