Theta and Riemann xi function representations from harmonic oscillator eigensolutions

Abstract

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.Comment: 15 pages, no figures, appears in Phys. Lett.