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A special value of the spectral zeta function of the non-commutative harmonic osciallators

Hiroyuki Ochiai
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Abstract

The non-commutative harmonic oscillator is a $2\times2$-system of harmonic oscillators with a non-trivial correlation. We write down explicitly the special value at $s=2$ of the spectral zeta function of the non-commutative harmonic oscillator in terms of the complete elliptic integral of the first kind, which is a special case of a hypergeometric function.

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BibTeXRIS

Hiroyuki Ochiai. 2005-07-06. A special value of the spectral zeta function of the non-commutative harmonic osciallators. https://arxiv.org/abs/math/0507111

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