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

2009/01/06 by Kazufumi Kimoto, Kimoto, Kazufumi · 1 citation
Mathematics · Physics and Astronomy · #Mathematical Analysis and Transform Methods #Quantum Mechanics and Applications #Quantum Mechanics and Non-Hermitian Physics #math.NT #msc:11A07 #msc:11M41

paper · pdf · doi:10.48550/arxiv.0901.0658

26 pages

arxiv created 2009/01/20 · arxiv updated 2009/12/01

Abstract

A generalization of the Apery-like numbers, which is used to describe the special values ζ_Q(2) and ζ_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.

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

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