On the spectral zeta function for the noncommutative harmonic oscillator

DOI10.1016/S0034-4877(07)80077-2zbMath1190.11047MaRDI QIDQ1002144

Masato Wakayama, Takashi Ichinose

Publication date: 24 February 2009

Published in: Reports on Mathematical Physics (Search for Journal in Brave)

zbMATH Keywords

spectral zeta function

Mathematics Subject Classification ID

Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Miscellaneous applications of number theory (11Z05) Selberg zeta functions and regularized determinants; applications to spectral theory, Dirichlet series, Eisenstein series, etc. (explicit formulas) (11M36)

Related Items (5)

Simplicity of the lowest eigenvalue of non-commutative harmonic oscillators and the Riemann scheme of a certain Heun's differential equation ⋮ Ultra-weak time operators of Schrödinger operators ⋮ On the spectral zeta function of second order semiregular non-commutative harmonic oscillators ⋮ Non-commutative harmonic oscillators and related problems ⋮ Spectral analysis of non-commutative harmonic oscillators: the lowest eigenvalue and no crossing

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Non-commutative harmonic oscillators and the connection problem for the Heun differential equation
• A proof that Euler missed. Apéry's proof of the irrationality of \(\zeta(3)\). An informal report
• Regularized products and determinants
• A special value of the spectral zeta function of the non-commutative harmonic oscillators
• Zeta functions for the spectrum of the non-commutative harmonic oscillators
• 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
• APÉRY-LIKE NUMBERS ARISING FROM SPECIAL VALUES OF SPECTRAL ZETA FUNCTIONS FOR NON-COMMUTATIVE HARMONIC OSCILLATORS
• Proprietes spectrales d'operators pseduo-differentiels
• Corrigenda and Remarks to Non-commutative harmonic oscillators-I
• ON THE SPECTRUM AND THE LOWEST EIGENVALUE OF CERTAIN NON-COMMUTATIVE HARMONIC OSCILLATORS
• VERIFIED NUMERICAL COMPUTATIONS FOR EIGENVALUES OF NON-COMMUTATIVE HARMONIC OSCILLATORS
• Non-commutative harmonic oscillators and Fuchsian ordinary differential operators

This page was built for publication: On the spectral zeta function for the noncommutative harmonic oscillator