07-52 Takashi Ichinose and Masato Wakayama

On the Spectral Zeta Function for the Non-commutative Harmonic Oscillator (35K, LaTeX 2e) Mar 4, 07

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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.

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