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

2009/03/30 by Kazufumi Kimoto, Kimoto, Kazufumi
Mathematics · Physics and Astronomy · #14G10 #35P99 #FOS: Mathematics #Mathematical Analysis and Transform Methods #Mathematical functions and polynomials #Number Theory (math.NT) #Quantum Mechanics and Non-Hermitian Physics #math.NT #msc:14G10 #msc:35P99

paper · pdf · doi:10.48550/arxiv.0903.5165

13 pages

arxiv created 2009/03/30 · openalex publication_date 2009/03/30 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We calculate the special values of the spectral zeta function of the non-commutative harmonic oscillator, and give a general formula for them as integrals of certain algebraic functions. This is a generalization of the result by Ichinose-Wakayama (2005), in which the first two special values are studied.

Citations

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

Related

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• A variation of multiple L-values arising from the spectral zeta function of the non-commutative harmonic oscillator
• Higher Apery-like numbers arising from special values of the spectral zeta function for the non-commutative harmonic oscillator
• On The Spectral Zeta Function Of Second Order Semiregular Non-Commutative Harmonic Oscillators
• Apéry-like numbers for non-commutative harmonic oscillators and automorphic integrals