Asymptotic analysis on a pseudo-Hermitian Riemann-zeta Hamiltonian

Abstract

The differential-equation eigenvalue problem associated with a recently-introduced Hamiltonian, whose eigenvalues correspond to the zeros of the Riemann zeta function, is analyzed using Fourier and WKB analysis. The Fourier analysis leads to a challenging open problem concerning the formulation of the eigenvalue problem in the momentum space. The WKB analysis gives the exact asymptotic behavior of the eigenfunction.

References in corpus (4)

• Hamiltonian for the zeros of the Riemann zeta function
• The Quantum Mellin transform
• H = x p with interaction and the Riemann zeros
• The Lerch zeta function IV. Hecke operators

Cited by in corpus (4)

• Supersymmetry and the Riemann zeros on the critical line
• Operator-valued zeta functions and Fourier analysis
• Supersymmetric quantum mechanics and the Riemann hypothesis
• Conformal bridge transformation, $\mathcal{P}\mathcal{T}$- and super- symmetry