Special value formula for the spectral zeta function of the non-commutative harmonic oscillator
Kazufumi Kimoto
TL;DR
This paper derives a general integral formula for the special values of the spectral zeta function of the non-commutative harmonic oscillator, extending previous specific cases.
Contribution
It provides a comprehensive formula for all special values of the spectral zeta function, generalizing prior results by Ichinose-Wakayama.
Findings
Derived integral representations for the spectral zeta function values.
Extended previous results to a broader class of special values.
Enhanced understanding of the spectral properties of non-commutative harmonic oscillators.
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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsQuantum Mechanics and Non-Hermitian Physics · Mathematical functions and polynomials · Mathematical Analysis and Transform Methods