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

Research output: Contribution to journalArticle

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Abstract

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.

Original languageEnglish
Pages (from-to)31-36
Number of pages6
JournalRamanujan Journal
Volume15
Issue number1
DOIs
Publication statusPublished - Jan 1 2008
Externally publishedYes

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Spectral Function
Harmonic Oscillator
Riemann zeta function
Elliptic integral of the first kind
Hypergeometric Functions

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

Cite this

A special value of the spectral zeta function of the non-commutative harmonic oscillators. / Ochiai, Hiroyuki.

In: Ramanujan Journal, Vol. 15, No. 1, 01.01.2008, p. 31-36.

Research output: Contribution to journalArticle

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