On The Spectral Zeta Function For The Noncommutative Harmonic Oscillator

金沢大学大学院自然科学研究科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\u27s 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. © 2007 Polish Scientific Publishers PWN, Warszawa