2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/75690The 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.5 pages, no figuresRepresentation TheoryNumber Theory11M36; 33C20text