TY - JOUR

T1 - On The Spectral Zeta Function For The Noncommutative Harmonic Oscillator

AU - Ichinose, Takashi

AU - Wakayama, Masato

N1 - Funding Information:
*Supported in part by JSPS Grant-in-Aid for Scientific Research (B) No. 16340038. tSupported in part by JSPS Grant-in-Aid for Scientific Research (B) No. 15340012.

PY - 2007/6

Y1 - 2007/6

N2 - The spectral zeta function for the so-called 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 ζ(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.

AB - The spectral zeta function for the so-called 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 ζ(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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U2 - 10.1016/S0034-4877(07)80077-2

DO - 10.1016/S0034-4877(07)80077-2

M3 - Article

AN - SCOPUS:36648999325

SN - 0034-4877

VL - 59

SP - 421

EP - 432

JO - Reports on Mathematical Physics

JF - Reports on Mathematical Physics

IS - 3

ER -