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

@inproceedings{Kimoto2008AprylikeNA,
  title={Ap{\'e}ry-like numbers arising from special values of spectral zeta functions for non-commutative harmonic oscillators},
  author={Kazufumi Kimoto and Masato Wakayama},
  year={2008}
}
We derive an expression for the value ζQ(3) of the spectral zeta function ζQ(s) studied in [10, 11] for the non-commutative harmonic oscillator defined in [17] 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 ζQ(3). We also show that the numbers J̃2(n) and J̃3(n) have congruence… CONTINUE READING

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