A special value of the spectral zeta function of the non-commutative harmonic oscillators

DOI10.1007/s11139-007-9065-1zbMath1149.11043arXivmath/0507111OpenAlexW1978187141MaRDI QIDQ2426705

Hiroyuki Ochiai

Publication date: 23 April 2008

Published in: The Ramanujan Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0507111

zbMATH Keywords

Heun's equationHarmonic oscillatorSpecial valuesSpectral zeta

Mathematics Subject Classification ID

Selberg zeta functions and regularized determinants; applications to spectral theory, Dirichlet series, Eisenstein series, etc. (explicit formulas) (11M36) Generalized hypergeometric series, ({}_pF_q) (33C20) Elliptic integrals as hypergeometric functions (33C75)

Related Items (9)

Determinant Expressions of Constraint Polynomials and the Spectrum of the Asymmetric Quantum Rabi Model ⋮ A variation of multiple $L$-values arising from the spectral zeta function of the non-commutative harmonic oscillator ⋮ Apéry-like numbers for non-commutative harmonic oscillators and automorphic integrals ⋮ Non-commutative harmonic oscillators and related problems ⋮ A supercongruence relation among Ap ⋮ On the spectrum of certain noncommutative harmonic oscillators ⋮ On the spectral zeta function for the noncommutative harmonic oscillator ⋮ Number Theoretic Study in Quantum Interactions ⋮ Non-commutative Harmonic Oscillators

Cites Work

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• Oscillator representations and systems of ordinary differential equations
• SPECIAL VALUES OF THE SPECTRAL ZETA FUNCTION OF THE NON-COMMUTATIVE HARMONIC OSCILLATOR AND CONFLUENT HEUN EQUATIONS
• Non-commutative harmonic oscillators-II
• THE MONODROMY OF THE PERIOD MAP OF A 4-PARAMETER FAMILY OF K3 SURFACES AND THE HYPERGEOMETRIC FUNCTION OF TYPE (3, 6)
• Non-commutative harmonic oscillators-I
• Non-commutative harmonic oscillators and Fuchsian ordinary differential operators

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