Apéry-like numbers arising from special values of spectral zeta functions for non-commutative harmonic oscillators
نویسندگان
چکیده
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 relations like those of the Apéry numbers.
منابع مشابه
Higher Apéry-like numbers arising from special values of the spectral zeta function for the non-commutative harmonic oscillator
A generalization of the Apéry-like numbers, which is used to describe the special values ζQ(2) and ζQ(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 Apéry-like numbers. We discuss several kin...
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