2005/07/06 by Hiroyuki Ochiai, Ochiai, Hiroyuki
Mathematics · Physics and Astronomy · #11M36 #33C20 #FOS: Mathematics #Mathematical functions and polynomials #Number Theory (math.NT) #Quantum Mechanics and Non-Hermitian Physics #Representation Theory (math.RT) #Spectral Theory in Mathematical Physics #math.NT #math.RT #msc:11M36 #msc:33C20
paper · pdf · doi:10.48550/arxiv.math/0507111
5 pages, no figures
arxiv created 2005/07/06 · openalex publication_date 2005/07/06 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The non-commutative harmonic oscillator is a 2×2-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.