Theta and Riemann xi function representations from harmonic oscillator eigensolutions

Details Theta and Riemann xi function representations from harmonic oscillator eigensolutions Theta and Riemann xi function representations from harmonic oscillator eigensolutions

2006-12-28

arxiv.org/abs/math-ph/0612086v1

Physics

Mathematical Physics

15 pages, no figures, appears in Phys. Lett. A

Scientific paper

10.1016/j.physleta.2006.10.055

From eigensolutions of the harmonic oscillator or Kepler-Coulomb Hamiltonian
we extend the functional equation for the Riemann zeta function and develop
integral representations for the Riemann xi function that is the completed
classical zeta function. A key result provides a basis for generalizing the
important Riemann-Siegel integral formula.

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