 0752 Takashi Ichinose and Masato Wakayama
 On the Spectral Zeta Function for the Noncommutative
Harmonic Oscillator
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Mar 4, 07

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Abstract. The spectral zeta function for the socalled noncommutative
harmonic oscillator
is able to be meromorphically extended to the whole complex
plane, having only one simple pole at the same point $s=1$ where
Riemann's zeta function $\zeta(s)$ has,
and possesses a trivial zero at each nonpositive even integer.
The essential part of its proof is sketched. A new result is also given
on the lower and upper bounds of the eigenvalues of the noncommutative
harmonic oscillator.
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