Higher Apery-like numbers arising from special values of the spectral zeta function for the non-commutative harmonic oscillator

Abstract

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.

arXiv comment26 pages

Cited by in corpus (1)

• Special value formula for the spectral zeta function of the non-commutative harmonic oscillator