%0 Journal Article
%T Higher Apery-like numbers arising from special values of the spectral zeta function for the non-commutative harmonic oscillator
%A Kazufumi Kimoto
%J Mathematics
%D 2009
%I arXiv
%X A generalization of the Apery-like numbers, which is used to describe the special values $\zeta_Q(2)$ and $\zeta_Q(3)$ of the spectral zeta function for the non-commutative harmonic oscillator, are introduced and studied. In fact, we give a recurrence relation for them, which shows a ladder structure among them. Further, we consider the `rational part' of the higher Apery-like numbers. We discuss several kinds of congruence relations among them, which are regarded as an analogue of the ones among Apery numbers.
%U http://arxiv.org/abs/0901.0658v2