Apéry-like numbers arising from special values of spectral zeta functions for non-commutative harmonic oscillators

Kazufumi Kimoto, Masato Wakayama

Research output: Contribution to journalArticle

15 Citations (Scopus)

Abstract

We derive an expression for the value ζQ(3) of the spectral zeta function ζQ(s) for the non-commutative harmonic oscillator using a Gaussian hypergeometric function. In this study, two sequences of rational numbers, denoted J̃2(n) and J̃3(n), which can be regarded as analogues of the Apéry numbers, naturally arise and play a key role in obtaining the expressions for the values ζQ(2) and ζ Q(3). We also show that the numbers J̃ 2(n) and J̃3(n) have congruence relations such as those of the Apéry numbers.

Original languageEnglish
Pages (from-to)383-404
Number of pages22
JournalKyushu Journal of Mathematics
Volume60
Issue number2
DOIs
Publication statusPublished - May 10 2007

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Spectral Function
Harmonic Oscillator
Riemann zeta function
Gaussian Hypergeometric Function
Congruence Relation
Analogue

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

Apéry-like numbers arising from special values of spectral zeta functions for non-commutative harmonic oscillators. / Kimoto, Kazufumi; Wakayama, Masato.

In: Kyushu Journal of Mathematics, Vol. 60, No. 2, 10.05.2007, p. 383-404.

Research output: Contribution to journalArticle

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