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

Kazufumi Kimoto, Masato Wakayama

研究成果: Contribution to journalArticle査読

18 被引用数 (Scopus)

抄録

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.

本文言語英語
ページ(範囲)383-404
ページ数22
ジャーナルKyushu Journal of Mathematics
60
2
DOI
出版ステータス出版済み - 5 10 2007
外部発表はい

All Science Journal Classification (ASJC) codes

  • 数学 (全般)

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