Takashi Ichinose and Masato Wakayama
On the Spectral Zeta Function for the Non-commutative
Harmonic Oscillator
(35K, LaTeX 2e)
ABSTRACT. The spectral zeta function for the so-called non-commutative
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 non-positive 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 non-commutative
harmonic oscillator.